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...tuples (a,b) and (b,a) are not equal, and the tuples (a,a) and (a) are not equal either. ...ltisets {a,b} and {b,a} are equal, but the multisets {a,a} and {a} are not equal. ...

...s of the pairs are equal, and also the second coordinates of the pairs are equal. ...

...nality of the set ''B'' is ''greater than or equal to'' (or ''more than or equal'' members) set ''B'' if and only if there is an injective function from ''A ...

...follows that the lengths of the pairs of sides opposite each other must be equal. A rectangle with all four sides equal in length is called a [[square (geometry)|square]]. ...

In [[algebra]], the '''discriminant''' of a [[polynomial]] that is equal to zero with [[real number|real]] or [[complex number|complex]] [[coefficie If the discriminant is equal to zero, then there are two repeating [[real numbers]], i.e. exactly one re ...

In all Parallelogram's opposite angles are equal to each other. *Two pairs of opposite sides are equal in length ...

...egular]] decagon, having all sides of equal length and each internal angle equal to 144°. ...

...i</math> and <math>\theta _r</math>) must be equal. Both angles have to be equal whenever reflection occurs. This is known as the "law of reflection". ...

...gle]]''' - A right-angled triangle is a triangle that has an angle that is equal to 90 degrees. (A triangle cannot have more than one right angle) The stand * '''Sine''' (sin) - The sine of an angle is equal to the <math>{\text{Opposite} \over \text{Hypotenuse}}</math><br /> ...

...]s of things can be ordered: Take the first element of a set, it is either equal to the element looked for, or there is an order relation that can be used t ...mple of a symmetric relation is "is equal to". If X "is equal to" Y, Y "is equal to" X. ...

...rface area and the time for planet 1 to cover segment ''A''₁ is equal to the time to cover segment ''A''₂. <br><br> (3) The total orbi #A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. ...

*for [[circular orbit]]s: <math>e\,\!</math> is equal to zero, *for parabolic trajectories: <math>e\,\!</math> is equal to 1, ...

Power is also equal to force times velocity (or speed). ...focus]] light. It is measured in [[dioptre]]s (inverse [[metre]]s), and is equal to one over the [[focal length]] of the optical device. ...

| equals, is equal to | approximately equal ...

...hematics)|function]] counting the number of [[prime number]]s less than or equal to some [[real number]] ''x''. It is written as <math>\pi(x)</math>, but it ...

* A finite number is a number which is not equal to <math>\pm\infty</math>; all [[real number]]s are finite. ...

...ound the [[equation]] for [[energy]]: [[E=mc²]]. This means that energy is equal to a certain amount of [[mass]]. However, this is a simplified version of h ...f light (which is "c" in this equation), <math>\frac{v^2}{c^2}</math> will equal one, and since that would leave one minus one in the denominator, there wou ...

The '''solar mass''' is a [[unit of measurement]] of [[mass]]. It is equal to the mass of the [[Sun]], about 332,950 times the mass of the [[Earth]], ...

One of the [[angle]]s of a [[right triangle]] is always equal to 90 [[degree (geometry)|degrees]]. This angle is the [[right angle]]. The ...s that the [[area]] of a [[square (geometry)|square]] on the hypotenuse is equal to the [[sum]] of the areas of the squares on the legs. In this picture, th ...

...ple, 2 is the square root of 4, because 2×2=4. Only numbers bigger than or equal to zero have real square roots. A number bigger than zero has two square ro ...efer most likely to the base of a square. As the sides of a square are all equal, the word radix may be interpreted as side of a square, even not literally ...

...(antiderivative) of a function f is another function F whose derivative is equal to the first function f. ...of a function f with respect to the variable t over the interval [a,x] is equal to the function f with respect to x. This describes the derivative and inte ...

...subsequence (not necessarily consecutive) of these integers, whose sum is equal to <math> 0 </math>. (Hint: Consider <math> b_i=a_i-i </math>) ...ubsets <math> A'\subseteq A </math> and <math> B'\subseteq B </math> with equal sum, i.e. <math>\sum\limits_{x\in A'}x=\sum\limits_{y\in B'}y </math> (Hint ...

...values so the output of the function at the first value is [[less than or equal to]] the second value. In math terms this means <math>(x,r) \in \operatorn ...

...lost, and so the kinetic energy of the two objects after the collision is equal to their total kinetic energy before the collision. Elastic collisions occu Setting the two equal gives us our first equation: ...

...e <math>x + 1</math> does not have one because <math>x + 1</math> is never equal to ''x''. ...

The diameter of a circle is equal to twice its radius (''d'' equals 2 times ''r''). ...ivided by ''d''). As a [[Fraction (mathematics)|fraction]] the number π is equal to about {{frac|22|7}} or 335/113 (which is closer) and as a number it is ...

...hey are equal to each other. That is not true when the thing they are both equal to is 0/0. This means that the normal rules of maths do not work when the n ...

...eld]]s. Tesla can be measured in different ways; for example, one tesla is equal to one [[weber (unit)|weber]] per square meter. Using other SI derived units, a tesla is also equal to: ...

If the exponent is equal to 2, then the power is called '''square''' because the [[area]] of a [[squ If the exponent is equal to 3, then the power is called '''cube''' because the [[volume]] of a [[cub ...

...rved]] object, meaning that the total initial momentum of a system must be equal to the total final momentum of a system. Total amount of '''momentum''' re The meaning is that the net force on an object is equal to the rate of change in momentum of the object. ...

...umber ''a''. The new ratio is (''a''+''b'')/''a''. If these two ratios are equal to the same number, then that number is called the '''golden ratio'''. The ...a'' is then <math>(\varphi+1)/\varphi</math>. Because these two ratios are equal, this is true: ...

...ller than ''b'', that is, it is either bigger, or [[Equality (mathematics)|equal]] to ''b'') ...eq b</math> means that ''a'' is not bigger than ''b'', or it is smaller or equal to ''b'') ...

...s|mass]] {{math|''m''}}, the net force {{math|'''F'''}} on the particle is equal to the mass {{math|''m''}} times the particle's [[w:acceleration|accelerati ...to be confused with ''G'', the universal gravitational constant), roughly equal to 9.8 meters per second² (32 feet per second²) on Ea ...

...d be 0, and so <math>cos\theta</math> would be 1. So the two equations are equal. ...

...relative to the entire <math>2\pi</math> encompassing one orbit is simply equal to ratio of the time of flight to the [[orbit]]al [[orbital period|period]] ...

...hat values will cause the [[:en:Fraction_(mathematics)|denominator]] to be equal to 0 because this will make the function undefined, and therefore not [[:en ...

...ion]] with value of the [[weighted average]] of 2 points is [[less than or equal to]] the weighted average of the function at those points. Also, a functio ...

For an ideal (without [[friction]]) mechanism, it is also equal to: ...

...[[symbol rate]]. If one [[symbol]] can be transmitted per second, this is equal to one Baud. The unit is named after [[Jean-Maurice-Émile Baudot]] a French ...

A '''fraction''' is a number that shows how many equal parts there are. When we write fractions, we show one number with a line ab #Think of a cake made of 4 equal parts. Each is 1 part of 4. In maths, you write this as <math>\tfrac{1}{4}< ...

* 1 Newton is equal to the amount of force required to accelerate an object at a rate or 1 metr ...

The DI is equal to the minimum inter-cluster distance divided by the maximum cluster size. ...

...w many [[9 (number)|nines]] there are before the [[ellipsis]], it is still equal to 1. ...9, meaning there is no number between 0.999... and 1. Therefore, they are equal. ...

{{cquote|The increase in the internal energy of a thermodynamic system is equal to the amount of [[heat|heat energy]] added to the system minus the [[Work ...n the surroundings, and to state that the total energy added by heating is equal to the sum of the increase in internal energy plus the work done by the sys ...

...[[moment of inertia]] (resistance to angular acceleration or deceleration, equal to the product of the mass and the square of its perpendicular distance fro ...

...[[moment of inertia]] (resistance to angular acceleration or deceleration, equal to the product of the mass and the square of its perpendicular distance fro ...

...s, a satellite must go fast enough it misses the ground. For the forces to equal each other, ...[Gravitational constant]]. To make a circle, the angular frequency must be equal to, ...

...very bin <math>i</math>, the expected load <math>\mathbf{E}[X_i]</math> is equal to the average load <math>m/n</math>. ...is within <math>O\left(\frac{m}{n}\right)</math>, which is asymptotically equal to the average load. ...

The [[SI]] unit of electric current is the [[ampere]] (A). This is equal to one [[coulomb]] of charge in one second. ...n is caused by temperature, and electrons flowing in one direction tend to equal the electrons flowing from the other direction, so this is not what causes ...

...to 5 + 5, or 2 is equal to 5 + 5, or 3 is equal to 5 + 5, ... , or 100 is equal to 5 + 5, or ..., etc. : For at least one [[natural number]] ''n'', ''n'' is equal to 5+5. ...

...segment from a vertex to an asymptote. The length of the conjugate axis is equal to ''2b''. ...

...nction]]. The prime counting function is the number of primes less than or equal to ''x''. ...

...oves 20 meters (m) to the left in 4 seconds (s), its velocity (v) would be equal to:<blockquote><math display="block">\text{v} = \frac\text{20 m}\text{4 s} ...

...e is the smallest electric charge found in a stable particle. A coulomb is equal to 6,241,509,629,152,650,000 elementary charges. The coulomb was named in h ...

...[[gas]]es at low pressures where the [[ideal gas law]] holds, fugacity is equal to pressure. The ratio <math> \phi = f/P \,</math> between fugacity <math>f ...

...h>S_n</math> uniformly at random. (All permutation are supposed to have an equal probability of selection.) ...

...th)]]''', '''<math>\pi</math>''', or '''π''', is the mathematical constant equal to a circle's circumference divided by its diameter. ...

In many situations ''c'' is equal to zero, for example when considering a [[Maclaurin series]]. ...

...zontal length under the part of the function you want to evaluate into "n" equal pieces. That is the n on top of the Σ (Greek letter [[sigma]]). The (x<su ...

...t is [[Measurement|measure]]<nowiki/>d in [[joules]] per second, which are equal to [[watt]]s. A watt is one unit of [[Power (physics)|power]]. Just as a [[ ...

It is a rotating body's resistance to angular acceleration or deceleration, equal to the product of the mass and the square of its perpendicular distance fro ...

...very vertex <math>v</math>, the sum of currents entering <math>v</math> is equal to the the sum of currents leaving <math>v</math>. ...<math>e=\{u,v\}</math> in the graph, the currents across <math>e</math> is equal to the difference of voltage between <math>u</math> and <math>v</math> over ...

...e range of the middle half of the scores. The scores are divided into four equal parts, separated by the [[quartile]]s <math>Q_1, Q_2</math> and <math>Q_3</ ...

The theorem says that the remainder will be equal to <math>(6)^2 - 2 \cdot (6) + 4 = 36 - 12 + 4 = 28.</math> ...

After that, '''g2''' is equal to <math>3\uparrow \uparrow \uparrow \uparrow \ldots \uparrow \uparrow \upa '''g3''' is equal to <math>3\uparrow \uparrow \uparrow \uparrow \uparrow \ldots \uparrow \upa ...

Where ''p'' is the [[momentum]]. (Momentum is equal to mass times velocity). These equations merely say that matter exhibits a ...

...ber if and only if one can compose a [[Square (geometry)|square]] of ''m'' equal (lesser) squares: ...xpression for the ''n''th square number is ''n''². This is also equal to the sum of the first ''n'' [[odd number]]s as can be seen in the above p ...

1 radian is equal to about 57.3°. There are 2[[Pi (mathematical constant)|π]] radians (about ...

...0</math>, which normally has no solution as the value of x^2 would have to equal -1. Though the problem is solvable, the square root of -1 could not be repr ...

...<math>b</math> and <math>c</math> are constants, and <math>a</math> is not equal to <math>0</math>. ...

...integer. There is no largest integer. Each integer is either larger than, equal to, or smaller than any integer. [[Consecutive integer]]s are integers that ...

...th>x</math>-values as we want, so long as we ''don't'' make <math>x</math> equal to <math>0</math>. For instance, we could make x=.00000001 or -.00000001, b ...

...is a central idea in [[evolution|evolutionary theory]]. Fitness is usually equal to the proportion of the individual's [[gene]]s in all the genes of the nex ...nesses of different individuals with the same genotype are not necessarily equal. It depends on the [[environment]] in which the individuals live, and on ac ...

...onstant)|e]]. The number ''e'' cannot be written exactly, but it is almost equal to 2.71828. ...than ''e''. The blue curve is an exponential function with a base exactly equal to ''e''. The red line is a [[Tangent (geometry)|tangent]] to the blue curv ...

...r <math>b</math> with <math>m</math> entries chosen independently and with equal probability from <math>\{-1,+1\}</math>, ...s, each <math>b_i</math> is either positive or negative independently with equal probability. There are expectedly <math>\mu=\frac{k}{2}</math> positive <ma ...

up and to the right, when two paths are considered equal if one can be two colors. Two colorings are equal if they arise from each other by a ...

'''D''' is equal to the diameter of the triangle's [[circumcircle]]. ...

...ion when they touch each other. A value of 1 means the frictional force is equal to the normal force. Some people think that the coefficient of friction can ...

The total reluctance is equal to the ratio of the "[[magnetomotive force]]” (MMF) in a passive [[magnetic :''<math>\mu_0</math>'' is the permeability of free space, equal to <math>4 \pi \times 10^{-7}</math> henry per metre ...

...You can take the [[square root]] of each side of the equation, since it is equal. However, any real square root has two answers. You can think of the negati ...became the Universe we see today. Physicists do not yet know for sure that equal amounts of matter and antimatter were created, and because of this, they ar ...

Ten megaseconds is equal to 115.74 days. 100 megaseconds is equal to 3.2 years. ...

('''pi''' is equal to the [[circumference]] divided by the [[diameter]]).|221x221px]] * 10 digits for a radius equal to that of the earth ...

...'r''}} in [[metre]]s (m), and the constant {{math|''G''}} is approximately equal to {{val|6.674|e=-11|u=N m² kg⁻²}}.<ref>{{cite journa ...

Split the [[plaintext]] block into two equal pieces, (<math>L_1</math>, <math>R_1</math>) ...modified structure where <math>L_1</math> and <math>R_1</math> are not of equal lengths. The [[MacGuffin (cipher)|MacGuffin cipher]] is an [[experiment]]al ...

...e form of {{math|''ax''² + ''bx'' + ''c''}}, where ''a'' is not equal to 0. It makes a [[parabola]] (a "U" shape) when graphed on a [[coordinate ...

...ving the [[floor function]], which gives the greatest integer less than or equal to a given number. ...

...e primes have a close connection to [[perfect number]]s, which are numbers equal to the sum of their proper divisors. Historically, the study of Mersenne pr ...

LC circuit's [[resonant frequency]] is equal to: <math>\omega=\sqrt{1\over LC}</math> ...

...nt of the gravitational force in this direction (''mg'' cos ''θ'') must be equal and opposite to normal force exerted by the plane, ''N''. Therefore <math>N ...

...the number: for instance, <math>23_8 \ </math>means 23 in base 8 (which is equal to 19 in base 10). ...

...he boat moves backward. Often, people say, ''For every action there is an equal and opposite reaction.'' ...

The sum of two matrices is the matrix, which (''i'',''j'')-th entry is equal to the sum of the (''i'',''j'')-th entries of two matrices: ...ferent dimensions, as long as the number of columns in the first matrix is equal to the number of rows in the second matrix. ...

...ssign a random value in <math>\{\mathrm{true},\mathrm{false}\}</math> with equal probability. For the <math>i</math>th clause, let <math>X_i</math> be the r ...\prod_{i=1}^k(1-y_i^*)</math> is minimized when all <math>y_i^*</math> are equal and <math>y_i^*=\frac{z_j^*}{k}</math>. Thus, the probability that <math>C_ ...

...ssign a random value in <math>\{\mathrm{true},\mathrm{false}\}</math> with equal probability. For the <math>i</math>th clause, let <math>X_i</math> be the r ...\prod_{i=1}^k(1-y_i^*)</math> is minimized when all <math>y_i^*</math> are equal and <math>y_i^*=\frac{z_j^*}{k}</math>. Thus, the probability that <math>C_ ...

...ædia Universalis]</ref> The equals sign says that both sides are exactly [[equal|the same]] value. An equation can be as simple as x=0, or as hard as 4(3y^9 ...

...rational numbers <math>\frac{a}{b}</math> and <math>\frac{c}{d}</math> are equal if <math>ad = bc</math>. ...

:<math>Do</math> is a reference diameter, equal to 1 [[Millimetre|mm]] (to make the equation dimensionally consistent.) ...

...math>A</math>) is [[Approximation|approximately]] [[Equality (mathematics)|equal]] to <math>N</math> ''(but how close? This needs to be expanded)''. ...

...ses to 42. The humidex tends to be higher than the U.S. [[heat index]] at equal temperature and relative humidity. ...

...ounds of the game, that is, the number of times the coin lands on heads is equal to the number of times it lands on tails. Compute <math>\sum_{i=1}^{+\infty ...e <math>{n-1\choose 2}</math> pairs of balls are chosen to be removed with equal probability). Find the following probabilities: ...

...t cause excitation. Note that the energy gained by the excited electron is equal to the energy of the incident [[photon]] (a particle of light), so only pho ...

...very bin <math>i</math>, the expected load <math>\mathbf{E}[X_i]</math> is equal to the average load <math>m/n</math>. ...is within <math>O\left(\frac{m}{n}\right)</math>, which is asymptotically equal to the average load. ...

...very bin <math>i</math>, the expected load <math>\mathbf{E}[X_i]</math> is equal to the average load <math>m/n</math>. ...is within <math>O\left(\frac{m}{n}\right)</math>, which is asymptotically equal to the average load. ...

Where the moment of inertia of center mass is equal to ...

The average vorticity in a small region of fluid flow is equal to the [[Circulation (fluid dynamics)|circulation]] <math>\Gamma</math> aro ...

...ounds of the game, that is, the number of times the coin lands on heads is equal to the number of times it lands on tails. Compute <math>\sum_{i=1}^{+\infty ...e <math>{n-1\choose 2}</math> pairs of balls are chosen to be removed with equal probability). Find the following probabilities: ...

...on]] of an [[atom]]. The number of [[electron]]s that can be in a shell is equal to <math>2n^2</math>. ...

...<math>G</math>, all vertices are connected, thus all <math>x_i</math> are equal. This shows that if <math>G</math> is connected, the eigenvalue <math>d=\la ...

...y</math>) two numbers (with division only allowed if <math>y</math> is not equal to zero). A field is a special [[ring (mathematics)|ring]], in which you ca ...

...each row is the row number. In a binomial expansion, this second number is equal to the power. (This makes the 'first' row, 1, actually the zero row). ...

...to b. Thus, the voltage from a to b + the voltage from b to c will always equal the voltage from a to c. ...

...e looking at two different bags. If they contain the same things, they are equal. ...where ''a'' and ''b'' are in the set of all [[integer]]s and ''b'' is not equal to 0. For example, <math>\begin{matrix} \frac{1}{4} \end{matrix} \in \mathb ...

...ill see that when random variables are independent, the variance of sum is equal to the sum of variances. To prove this, we first establish a very useful re ...

...ide of the augmented matrix are the constant terms each linear equation is equal to. For this system, the augmented matrix is: ...

...>m\times n</math> 0-1 matrix. The ''maximum'' number of independent 1's is equal to the ''minimum'' number of rows and columns required to cover all the 1's ...t we can break <math>P</math> into? Dilworth's theorem tells us that it is equal to the size of the maximum antichain. ...

...>m\times n</math> 0-1 matrix. The ''maximum'' number of independent 1's is equal to the ''minimum'' number of rows and columns required to cover all the 1's ...t we can break <math>P</math> into? Dilworth's theorem tells us that it is equal to the size of the maximum antichain. ...

...s in [[electrostatics]]. Consider a bar magnet which has magnetic poles of equal magnitude but opposite [[Polarity (physics)|polarity]]. Each pole is the so The ratio of these two non-equivalent CGS units (EMU/ESU) is equal exactly to the [[speed of light|speed of light in free space]], expressed i ...

:The size of a maximum matching in <math>G</math> is equal to the value of a maximum <math>s</math>-<math>t</math> flow in <math>G'</m :The size of a minimum vertex cover in <math>G</math> is equal to the value of a minimum <math>s</math>-<math>t</math> cut in <math>G'</ma ...

...ath>A</math>, denoted by <math>m</math>. Since all the row and column sums equal to some <math>\gamma>0</math>, there are at least <math>n</math> such entri ...>m\times n</math> 0-1 matrix. The ''maximum'' number of independent 1's is equal to the ''minimum'' number of rows and columns required to cover all the 1's ...

...ath>A</math>, denoted by <math>m</math>. Since all the row and column sums equal to some <math>\gamma>0</math>, there are at least <math>n</math> such entri ...>m\times n</math> 0-1 matrix. The ''maximum'' number of independent 1's is equal to the ''minimum'' number of rows and columns required to cover all the 1's ...

...of the pattern is 0, the second number is 1, and each number after that is equal to adding the two numbers right before it together. For example 0+1=1 and 3 ...

...ithmic scale is defined filling in the ranges between the semitones of the equal tempered scale in a compatible way. This scale corresponds to the note numb ...

...is number has the property that it divides a set of observed values in two equal halves, so that half of the values are below it, and half are above. ...

...[[vacuum]], all photons move at the [[speed of light]], '''c''', which is equal to 299,792,458 meters (approximately 300,000 kilometers) per second. ...

The variance of the sum of pairwise independent random variables is equal to the sum of variances. ...

The variance of the sum of pairwise independent random variables is equal to the sum of variances. ...

The variance of the sum of pairwise independent random variables is equal to the sum of variances. ...

The variance of the sum of pairwise independent random variables is equal to the sum of variances. ...

The variance of the sum of pairwise independent random variables is equal to the sum of variances. ...

The variance of the sum of pairwise independent random variables is equal to the sum of variances. ...

The variance of the sum of pairwise independent random variables is equal to the sum of variances. ...

...er in 2008). Since the amount of mass-energy created by the Higgs field is equal to the amount of kinetic-energy that the gauge boson lost by being slowed, ...

...>m\times n</math> 0-1 matrix. The ''maximum'' number of independent 1's is equal to the ''minimum'' number of rows and columns required to cover all the 1's ...t we can break <math>P</math> into? Dilworth's theorem tells us that it is equal to the size of the maximum antichain. ...

...>m\times n</math> 0-1 matrix. The ''maximum'' number of independent 1's is equal to the ''minimum'' number of rows and columns required to cover all the 1's ...t we can break <math>P</math> into? Dilworth's theorem tells us that it is equal to the size of the maximum antichain. ...

...>m\times n</math> 0-1 matrix. The ''maximum'' number of independent 1's is equal to the ''minimum'' number of rows and columns required to cover all the 1's ...t we can break <math>P</math> into? Dilworth's theorem tells us that it is equal to the size of the maximum antichain. ...

...>m\times n</math> 0-1 matrix. The ''maximum'' number of independent 1's is equal to the ''minimum'' number of rows and columns required to cover all the 1's ...t we can break <math>P</math> into? Dilworth's theorem tells us that it is equal to the size of the maximum antichain. ...

...>m\times n</math> 0-1 matrix. The ''maximum'' number of independent 1's is equal to the ''minimum'' number of rows and columns required to cover all the 1's ...t we can break <math>P</math> into? Dilworth's theorem tells us that it is equal to the size of the maximum antichain. ...

...r <math>b</math> with <math>m</math> entries chosen independently and with equal probability from <math>\{-1,+1\}</math>, ...s, each <math>b_i</math> is either positive or negative independently with equal probability. There are expectedly <math>\mu=\frac{k}{2}</math> positive <ma ...

If the impedance of the source, cable and load are not all equal, then a fraction of the signal is reflected back to the source, wasting pow ...

...up> ions (also written [H₃O⁺],<ref name=explan/> the equal concentration of [[:en:Hydronium|hydronium]] ions), measured in [[mole (uni ...

...r <math>b</math> with <math>m</math> entries chosen independently and with equal probability from <math>\{-1,+1\}</math>, ...s, each <math>b_i</math> is either positive or negative independently with equal probability. There are expectedly <math>\mu=\frac{k}{2}</math> positive <ma ...

For example, if <math>P_{[a,b]}</math> is equal to .5, then there is a 50% chance of finding the particle within that regio ...

...let <math>Y=\sum_{i=1}^m Y_i</math> be the number of <math>Y_i</math> that equal 1. ...

...let <math>Y=\sum_{i=1}^m Y_i</math> be the number of <math>Y_i</math> that equal 1. ...

...ery one of <math>\{a_i, a_{i+1}, \ldots, a_{j-1}, a_{j}\}</math> is chosen equal-probably.''' ...

...ery one of <math>\{a_i, a_{i+1}, \ldots, a_{j-1}, a_{j}\}</math> is chosen equal-probably.''' ...minimum cut is the minimum <math>s</math>-<math>t</math> min-cut, which is equal to the minimum <math>s</math>-<math>t</math> max-flow. ...

...ery one of <math>\{a_i, a_{i+1}, \ldots, a_{j-1}, a_{j}\}</math> is chosen equal-probably.''' ...very bin <math>i</math>, the expected load <math>\mathbf{E}[X_i]</math> is equal to the average load <math>m/n</math>. ...

...minimum cut is the minimum <math>s</math>-<math>t</math> min-cut, which is equal to the minimum <math>s</math>-<math>t</math> max-flow. ...

...very bin <math>i</math>, the expected load <math>\mathbf{E}[X_i]</math> is equal to the average load <math>m/n</math>. ...is within <math>O\left(\frac{m}{n}\right)</math>, which is asymptotically equal to the average load. ...

...very bin <math>i</math>, the expected load <math>\mathbf{E}[X_i]</math> is equal to the average load <math>m/n</math>. ...is within <math>O\left(\frac{m}{n}\right)</math>, which is asymptotically equal to the average load. ...

...very bin <math>i</math>, the expected load <math>\mathbf{E}[X_i]</math> is equal to the average load <math>m/n</math>. ...is within <math>O\left(\frac{m}{n}\right)</math>, which is asymptotically equal to the average load. ...

...very bin <math>i</math>, the expected load <math>\mathbf{E}[X_i]</math> is equal to the average load <math>m/n</math>. ...is within <math>O\left(\frac{m}{n}\right)</math>, which is asymptotically equal to the average load. ...

...very bin <math>i</math>, the expected load <math>\mathbf{E}[X_i]</math> is equal to the average load <math>m/n</math>. ...is within <math>O\left(\frac{m}{n}\right)</math>, which is asymptotically equal to the average load. ...

...i>{{|}|{|}}, or {0|0}</nowiki>. The first player to move will win. Games equal to {0|0} are very important. They are written with the symbol, '''*''' (st ...

Due to Axiom (K4), <math>\Pr(\bar{A})+\Pr(A)=\Pr(\Omega)</math> which is equal to 1 according to Axiom (K3), thus <math>\Pr(\bar{A})+\Pr(A)=1</math>. The ...

:The size of a maximum matching in <math>G</math> is equal to the value of a maximum <math>s</math>-<math>t</math> flow in <math>G'</m :The size of a minimum vertex cover in <math>G</math> is equal to the value of a minimum <math>s</math>-<math>t</math> cut in <math>G'</ma ...

:The size of a maximum matching in <math>G</math> is equal to the value of a maximum <math>s</math>-<math>t</math> flow in <math>G'</m :The size of a minimum vertex cover in <math>G</math> is equal to the value of a minimum <math>s</math>-<math>t</math> cut in <math>G'</ma ...

...ers of subsets of an <math>n</math>-set of even and of odd cardinality are equal. which is equal to the number of ways of choosing <math>k-1</math> slots out of <math>n-1</ ...

:The size of a maximum matching in <math>G</math> is equal to the value of a maximum <math>s</math>-<math>t</math> flow in <math>G'</m :The size of a minimum vertex cover in <math>G</math> is equal to the value of a minimum <math>s</math>-<math>t</math> cut in <math>G'</ma ...

Note that the left-eigenvalues are equal to the right-eigenvalues, because ...er the action of transition, but also when the chain is stationary, it has equal chance to move from <math>i</math> to <math>j</math> and from <math>j</math ...

then <math>b^0</math> must equal one, ...

The combination with an equal sign, <math>:=\,</math>, is used for [[definition]]s. ...

...into two equal piles without checking all combinations. The question "Is P equal to NP?" is a [[shorthand]] for asking if any method like that can exist. ...

...r <math>b</math> with <math>m</math> entries chosen independently and with equal probability from <math>\{-1,+1\}</math>, ...s, each <math>b_i</math> is either positive or negative independently with equal probability. There are expectedly <math>\mu=\frac{k}{2}</math> positive <ma ...

...number in the function's [[domain]]. If the Taylor Series of a function is equal to that function, the function is called an "[[analytic]] function." ...

...r <math>b</math> with <math>m</math> entries chosen independently and with equal probability from <math>\{-1,+1\}</math>, ...s, each <math>b_i</math> is either positive or negative independently with equal probability. There are expectedly <math>\mu=\frac{k}{2}</math> positive <ma ...

...)</math>'s are all symmetric, thus all <math>\mathbf{E}[T(e)]</math>'s are equal. The number of edges in the hypercube is <math>\frac{dN}{2}</math>. Therefo ...r <math>b</math> with <math>m</math> entries chosen independently and with equal probability from <math>\{-1,+1\}</math>, ...

...ill see that when random variables are independent, the variance of sum is equal to the sum of variances. To prove this, we first establish a very useful re ...{n}{2}\right\rceil</math> elements in <math>S</math> that are less than or equal to the median. The probability that <math>Y_i=1</math> is ...

.... This is because when finding the [[derivative]] of a function, constants equal 0, as in the function ...

...th>. However, as long as the game is fair, namely, winning and losing with equal chances, conditioning on the past variables <math>X_0,\ldots,X_{i-1}</math> ...

...al [[potential energy]] lost by the weight in descending was approximately equal to the thermal energy ([[heat]]) gained by the water by [[friction]] with t ...

...how that the expected running time of randomized quicksort on any input is equal to the average-case complexity of deterministic quicksort. Formally, we hav ...hus, the expected complexity of randomized quicksort on any fixed input is equal to the expected complexity of deterministic quicksort on a random input. Th ...

...ers of subsets of an <math>n</math>-set of even and of odd cardinality are equal. which is equal to the number of ways of choosing <math>k-1</math> slots out of <math>n-1</ ...

...ers of subsets of an <math>n</math>-set of even and of odd cardinality are equal. which is equal to the number of ways of choosing <math>k-1</math> slots out of <math>n-1</ ...

...ers of subsets of an <math>n</math>-set of even and of odd cardinality are equal. which is equal to the number of ways of choosing <math>k-1</math> slots out of <math>n-1</ ...

...ers of subsets of an <math>n</math>-set of even and of odd cardinality are equal. which is equal to the number of ways of choosing <math>k-1</math> slots out of <math>n-1</ ...

...ers of subsets of an <math>n</math>-set of even and of odd cardinality are equal. which is equal to the number of ways of choosing <math>k-1</math> slots out of <math>n-1</ ...

...ers of subsets of an <math>n</math>-set of even and of odd cardinality are equal. which is equal to the number of ways of choosing <math>k-1</math> slots out of <math>n-1</ ...

...ers of subsets of an <math>n</math>-set of even and of odd cardinality are equal. which is equal to the number of ways of choosing <math>k-1</math> slots out of <math>n-1</ ...

...ers of subsets of an <math>n</math>-set of even and of odd cardinality are equal. which is equal to the number of ways of choosing <math>k-1</math> slots out of <math>n-1</ ...

...ers of subsets of an <math>n</math>-set of even and of odd cardinality are equal. which is equal to the number of ways of choosing <math>k-1</math> slots out of <math>n-1</ ...

...umerical]] value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit form. For example, US$23.74 co ...ch other, and the expected (average) value of the rounded numbers would be equal to the expected value of the original numbers. ...

...{n}{2}\right\rceil</math> elements in <math>S</math> that are less than or equal to the median. The probability that <math>Y_i=1</math> is ...

...very bin <math>i</math>, the expected load <math>\mathbf{E}[X_i]</math> is equal to the average load <math>m/n</math>. ...is within <math>O\left(\frac{m}{n}\right)</math>, which is asymptotically equal to the average load. ...

...ill see that when random variables are independent, the variance of sum is equal to the sum of variances. To prove this, we first establish a very useful re ...{n}{2}\right\rceil</math> elements in <math>S</math> that are less than or equal to the median. The probability that <math>Y_i=1</math> is ...

:* independently choose one of <math>S</math> and <math>T</math> with equal probability, and let <math>v</math> join the chosen set. ...

...ed to this pivot. Cards with a smaller number go to stack B, those with an equal or bigger number go to stack C. ...

...math> is in every position of the randomly reordered <math>\pi</math> with equal probability <math>\frac{1}{n}</math>. The expected number of accesses made ...uniform, <math>x</math> appears in each position of <math>\pi</math> with equal probability. Due to Lemma 1, assuming that <math>x</math> is in the <math>k ...

...<math>G</math>, all vertices are connected, thus all <math>x_i</math> are equal. This shows that if <math>G</math> is connected, the eigenvalue <math>d=\la Note that the left-eigenvalues are equal to the right-eigenvalues, because ...

...ssign a random value in <math>\{\mathrm{true},\mathrm{false}\}</math> with equal probability. For the <math>i</math>th clause, let <math>X_i</math> be the r ...\prod_{i=1}^k(1-y_i^*)</math> is minimized when all <math>y_i^*</math> are equal and <math>y_i^*=\frac{z_j^*}{k}</math>. Thus, the probability that <math>C_ ...

...ssign a random value in <math>\{\mathrm{true},\mathrm{false}\}</math> with equal probability. For the <math>i</math>th clause, let <math>X_i</math> be the r ...\prod_{i=1}^k(1-y_i^*)</math> is minimized when all <math>y_i^*</math> are equal and <math>y_i^*=\frac{z_j^*}{k}</math>. Thus, the probability that <math>C_ ...

...e molecule, an identical atom exists diametrically opposite this center an equal distance from it. There may or may not be an atom at the center. Examples a ...rreducible representations. The tables are square because there are always equal numbers of irreducible representations and groups of symmetry operations. ...

...very bin <math>i</math>, the expected load <math>\mathbf{E}[X_i]</math> is equal to the average load <math>m/n</math>. ...is within <math>O\left(\frac{m}{n}\right)</math>, which is asymptotically equal to the average load. ...

...ill see that when random variables are independent, the variance of sum is equal to the sum of variances. To prove this, we first establish a very useful re ...{n}{2}\right\rceil</math> elements in <math>S</math> that are less than or equal to the median. The probability that <math>Y_i=1</math> is ...

...ill see that when random variables are independent, the variance of sum is equal to the sum of variances. To prove this, we first establish a very useful re ...{n}{2}\right\rceil</math> elements in <math>S</math> that are less than or equal to the median. The probability that <math>Y_i=1</math> is ...

...>f(\{a,b,c\}), f(\{a,b,d\}), f(\{a,c,d\}), f(\{b,c,d\})\,</math> cannot be equal, contradicting that all members of <math>{Y\choose 3}</math> have the same ...be iteratively applied to <math>n</math> before the result is less than or equal to 1. ...

...very bin <math>i</math>, the expected load <math>\mathbf{E}[X_i]</math> is equal to the average load <math>m/n</math>. ...is within <math>O\left(\frac{m}{n}\right)</math>, which is asymptotically equal to the average load. ...

...</math>. And due to the symmetry, all <math>\mathbf{E}[Y_i^2]</math>'s are equal. Thus, <math>\mathbf{E}[Y_i^2]=\frac{1}{d}</math> for all <math>i</math>. T ...

...</math>. And due to the symmetry, all <math>\mathbf{E}[Y_i^2]</math>'s are equal. Thus, <math>\mathbf{E}[Y_i^2]=\frac{1}{d}</math> for all <math>i</math>. T ...

...)</math>'s are all symmetric, thus all <math>\mathbf{E}[T(e)]</math>'s are equal. The number of edges in the hypercube is <math>\frac{dN}{2}</math>. Therefo ...

where ''B'' is a number that Balmer determined to be equal to 364.56&nbsp;nm. where ''R'' is the [[Rydberg constant]], equal to 0.0110&nbsp;nm⁻¹, and ''n'' must be greater than ''m''. ...

...minimum cut is the minimum <math>s</math>-<math>t</math> min-cut, which is equal to the minimum <math>s</math>-<math>t</math> max-flow. ...

[<strong>Tossing coins</strong>] We repeatedly toss a fair coin (with an equal probability of heads and tails). Let the random variable <math>X</math> be ...

Due to Axiom (A4), <math>\Pr(\bar{A})+\Pr(A)=\Pr(\Omega)</math> which is equal to 1 according to Axiom (A3), thus <math>\Pr(\bar{A})+\Pr(A)=1</math>. The ...

...by ''b'', where the numbers ''a'' and ''b'' are integers, and ''b'' is not equal to 0. ...

...th>. However, as long as the game is fair, namely, winning and losing with equal chances, conditioning on the past variables <math>X_0,\ldots,X_{i-1}</math> ...from the origin, and at each step moves to one of the four directions with equal probability. Let <math>X_i</math> be the distance from the origin, measured ...

:* independently choose one of <math>S</math> and <math>T</math> with equal probability, and let <math>v</math> join the chosen set. ...ssign a random value in <math>\{\mathrm{true},\mathrm{false}\}</math> with equal probability. For the <math>i</math>th clause, let <math>X_i</math> be the r ...

| surface_grav=0.0025<ref>With asteroid mass ''m'', radius ''r'' and ''G'' equal to the [[gravitational constant]], [[Newton's law of universal gravitation] ...

...<math>G</math>, all vertices are connected, thus all <math>x_i</math> are equal. This shows that if <math>G</math> is connected, the eigenvalue <math>d=\al ...

...>f(\{a,b,c\}), f(\{a,b,d\}), f(\{a,c,d\}), f(\{b,c,d\})\,</math> cannot be equal, contradicting that all members of <math>{Y\choose 3}</math> have the same ...

...>f(\{a,b,c\}), f(\{a,b,d\}), f(\{a,c,d\}), f(\{b,c,d\})\,</math> cannot be equal, contradicting that all members of <math>{Y\choose 3}</math> have the same ...

...>f(\{a,b,c\}), f(\{a,b,d\}), f(\{a,c,d\}), f(\{b,c,d\})\,</math> cannot be equal, contradicting that all members of <math>{Y\choose 3}</math> have the same ...

...>f(\{a,b,c\}), f(\{a,b,d\}), f(\{a,c,d\}), f(\{b,c,d\})\,</math> cannot be equal, contradicting that all members of <math>{Y\choose 3}</math> have the same ...

...>f(\{a,b,c\}), f(\{a,b,d\}), f(\{a,c,d\}), f(\{b,c,d\})\,</math> cannot be equal, contradicting that all members of <math>{Y\choose 3}</math> have the same ...

...>f(\{a,b,c\}), f(\{a,b,d\}), f(\{a,c,d\}), f(\{b,c,d\})\,</math> cannot be equal, contradicting that all members of <math>{Y\choose 3}</math> have the same ...

'Identity' refers to the property of a number that it is equal to itself. In other words, there exists an operation of two numbers so that ...

which is equal to the definition of <math>L</math>. ...

which is equal to the definition of <math>L</math>. ...

which is equal to the definition of <math>L</math>. ...

which is equal to the definition of <math>L</math>. ...

which is equal to the definition of <math>L</math>. ...

which is equal to the definition of <math>L</math>. ...

which is equal to the definition of <math>L</math>. ...

which is equal to the definition of <math>L</math>. ...

It is obvious that the two terms are equal, since we just count the same thing twice with different methods. The lemma ...

It is obvious that the two terms are equal, since we just count the same thing twice with different methods. The lemma ...

It is obvious that the two terms are equal, since we just count the same thing twice with different methods. The lemma ...

It is obvious that the two terms are equal, since we just count the same thing twice with different methods. The lemma ...

It is obvious that the two terms are equal, since we just count the same thing twice with different methods. The lemma ...

It is obvious that the two terms are equal, since we just count the same thing twice with different methods. The lemma ...

It is obvious that the two terms are equal, since we just count the same thing twice with different methods. The lemma ...

It is obvious that the two terms are equal, since we just count the same thing twice with different methods. The lemma ...

...very vertex <math>v</math>, the sum of currents entering <math>v</math> is equal to the the sum of currents leaving <math>v</math>. ...<math>e=\{u,v\}</math> in the graph, the currents across <math>e</math> is equal to the difference of potential between <math>u</math> and <math>v</math> ov ...

...very vertex <math>v</math>, the sum of currents entering <math>v</math> is equal to the the sum of currents leaving <math>v</math>. ...<math>e=\{u,v\}</math> in the graph, the currents across <math>e</math> is equal to the difference of potential between <math>u</math> and <math>v</math> ov ...

...very vertex <math>v</math>, the sum of currents entering <math>v</math> is equal to the the sum of currents leaving <math>v</math>. ...<math>e=\{u,v\}</math> in the graph, the currents across <math>e</math> is equal to the difference of potential between <math>u</math> and <math>v</math> ov ...

The [[electromotive force]] is equal to the value of this integral. Sometimes this symbol is used for the [[elec ...

...>f(\{a,b,c\}), f(\{a,b,d\}), f(\{a,c,d\}), f(\{b,c,d\})\,</math> cannot be equal, contradicting that all members of <math>{Y\choose 3}</math> have the same ...

...two''' possible values <math>\{0,1\}</math> for <math>r_j</math> which are equal-probable, so with at least <math>\frac{1}{2}</math> probability, the choice ...

* The values ''m'' = 0 or ''m'' = 1 always produce ciphertexts equal to 0 or 1 respectively, due to the properties of exponentiation. ...

...ery one of <math>\{a_i, a_{i+1}, \ldots, a_{j-1}, a_{j}\}</math> is chosen equal-probably.''' ...

...very bin <math>i</math>, the expected load <math>\mathbf{E}[X_i]</math> is equal to the average load <math>m/n</math>. ...is within <math>O\left(\frac{m}{n}\right)</math>, which is asymptotically equal to the average load. ...

...maximal value of <math>S</math> is attained when all nonzero weights are equal and concentrated on a clique. ...

...maximal value of <math>S</math> is attained when all nonzero weights are equal and concentrated on a clique. ...

...maximal value of <math>S</math> is attained when all nonzero weights are equal and concentrated on a clique. ...

...maximal value of <math>S</math> is attained when all nonzero weights are equal and concentrated on a clique. ...

...maximal value of <math>S</math> is attained when all nonzero weights are equal and concentrated on a clique. ...

In other words, if matrix ''A'' times the vector '''v''' is equal to the scalar ''λ'' times the vector '''v''', then ''λ'' is the eigenvalue ...

...ly beautiful result is that the optimums of the primal LP and its dual are equal. This is called the strong duality theorem of linear programming. ...

...th>. However, as long as the game is fair, namely, winning and losing with equal chances, conditioning on the past variables <math>X_0,\ldots,X_{i-1}</math> ...</math>. And due to the symmetry, all <math>\mathbf{E}[Y_i^2]</math>'s are equal. Thus, <math>\mathbf{E}[Y_i^2]=\frac{1}{d}</math> for all <math>i</math>. T ...

...maximal value of <math>S</math> is attained when all nonzero weights are equal and concentrated on a clique. ...

...maximal value of <math>S</math> is attained when all nonzero weights are equal and concentrated on a clique. ...

...maximal value of <math>S</math> is attained when all nonzero weights are equal and concentrated on a clique. ...

...maximal value of <math>S</math> is attained when all nonzero weights are equal and concentrated on a clique. ...

...er_theorem prime number theorem], the number of prime numbers less than or equal to <math>n</math> is <math>\pi(n)\sim\frac{n}{\ln n}</math>. This scheme wi ...

...minimum cut is the minimum <math>s</math>-<math>t</math> min-cut, which is equal to the minimum <math>s</math>-<math>t</math> max-flow. ...

...two''' possible values <math>\{0,1\}</math> for <math>r_j</math> which are equal-probable, so with at least <math>\frac{1}{2}</math> probability, the choice ...

...ill see that when random variables are independent, the variance of sum is equal to the sum of variances. To prove this, we first establish a very useful re ...

...ill see that when random variables are independent, the variance of sum is equal to the sum of variances. To prove this, we first establish a very useful re ...

...=1}^k(1-\hat{y}_i)</math> is minimized when all <math>\hat{y}_i</math> are equal and <math>\hat{y}_i=\hat{z}_j/k</math>. Thus, the probability that <math>C_ ...

...>f(\{a,b,c\}), f(\{a,b,d\}), f(\{a,c,d\}), f(\{b,c,d\})\,</math> cannot be equal, contradicting that all members of <math>{Y\choose 3}</math> have the same ...

It is obvious that the two terms are equal, since we just count the same thing twice with different methods. The lemma ...

...</math>. And due to the symmetry, all <math>\mathbf{E}[Y_i^2]</math>'s are equal. Thus, <math>\mathbf{E}[Y_i^2]=\frac{1}{d}</math> for all <math>i</math>. T ...

...th>. However, as long as the game is fair, namely, winning and losing with equal chances, conditioning on the past variables <math>X_0,\ldots,X_{i-1}</math> ...

which by independence between different hash functions and by symmetry is equal to: ...

which by independence between different hash functions and by symmetry is equal to: ...

which by independence between different hash functions and by symmetry is equal to: ...

which by independence between different hash functions and by symmetry is equal to: ...

which by independence between different hash functions and by symmetry is equal to: ...

...minimum cut is the minimum <math>s</math>-<math>t</math> min-cut, which is equal to the minimum <math>s</math>-<math>t</math> max-flow. ...

...ly beautiful result is that the optimums of the primal LP and its dual are equal. This is called the strong duality theorem of linear programming. ...

...th>. However, as long as the game is fair, namely, winning and losing with equal chances, conditioning on the past variables <math>X_0,\ldots,X_{i-1}</math> ...

...ms which generate uniform stationary distribution, <math>P_{uv}</math> are equal for all <math>uv\in E</math> and <math>1/P_{uv}</math> can be made <math>\l ...

| It is the value of a larger value divided by a smaller value if this is equal to the value of the sum of the values divided by the larger value. ...

...e multiplicities of every element in <math>A</math> and <math>B</math> are equal. ...

...e multiplicities of every element in <math>A</math> and <math>B</math> are equal. ...

...e multiplicities of every element in <math>A</math> and <math>B</math> are equal. ...

...e multiplicities of every element in <math>A</math> and <math>B</math> are equal. ...

...e multiplicities of every element in <math>A</math> and <math>B</math> are equal. ...

...e multiplicities of every element in <math>A</math> and <math>B</math> are equal. ...

...e multiplicities of every element in <math>A</math> and <math>B</math> are equal. ...

It is obvious that the two terms are equal, since we just count the same thing twice with different methods. The lemma ...

...<math>G</math>, all vertices are connected, thus all <math>x_i</math> are equal. This shows that if <math>G</math> is connected, the eigenvalue <math>d=\la ...

...th>. However, as long as the game is fair, namely, winning and losing with equal chances, conditioning on the past variables <math>X_0,\ldots,X_{i-1}</math> ...

...th>. However, as long as the game is fair, namely, winning and losing with equal chances, conditioning on the past variables <math>X_0,\ldots,X_{i-1}</math> ...

...th>. However, as long as the game is fair, namely, winning and losing with equal chances, conditioning on the past variables <math>X_0,\ldots,X_{i-1}</math> ...

...th>. However, as long as the game is fair, namely, winning and losing with equal chances, conditioning on the past variables <math>X_0,\ldots,X_{i-1}</math> ...

...th>. However, as long as the game is fair, namely, winning and losing with equal chances, conditioning on the past variables <math>X_0,\ldots,X_{i-1}</math> ...

...th>. However, as long as the game is fair, namely, winning and losing with equal chances, conditioning on the past variables <math>X_0,\ldots,X_{i-1}</math> ...

...th>. However, as long as the game is fair, namely, winning and losing with equal chances, conditioning on the past variables <math>X_0,\ldots,X_{i-1}</math> ...

...<math>G</math>, all vertices are connected, thus all <math>x_i</math> are equal. This shows that if <math>G</math> is connected, the eigenvalue <math>d=\la ...

...k is another word for energy. This means gravitational potential energy is equal to ...

...e multiplicities of every element in <math>A</math> and <math>B</math> are equal. ...

...<math>G</math>, all vertices are connected, thus all <math>x_i</math> are equal. This shows that if <math>G</math> is connected, the eigenvalue <math>d=\la ...

...t contains a cube of width <math>r</math>. The parameter <math>L</math> is equal to <math>\log\frac{R}{r}</math>. ...

which by independence between different hash functions and by symmetry is equal to: ...

...of error in position (x) times the range of error in momentum (p) is about equal to or greater than the [[dirac constant plancks constant divided by 4pi ]]. ...