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...t in a value of [[infinity]], which is itself undefined. Usually when two numbers are equal to the same thing, they are equal to each other. That is not true ...] in computer programming. Dividing [[Floating point unit|floating point]] numbers (decimals) by zero will usually result in either [[infinity]] or a special ...

...th>k</math>. Let <math>S</math> be a set with <math>|S|=n</math>. Find the numbers of <math>k</math>-tuples <math>(T_1,T_2,\dots,T_k)</math> of subsets <math> Let <math>p</math> be a prime integer and <math>a</math> be a positive integer. Show '''combinatorially''' that <math>a^p-a</math> is divisible by ...

...|300px|upright=1.2|The coloring of the complex function-values used above: positive real values are presented in red.]] ...ecause of its relation to the [[prime number theorem|distribution of prime numbers]]. It also has applications in other areas such as [[physics]], [[probabili ...

...an then be represented by a stream of Gödel numbers (also called effective numbers). [[Rogers' equivalence theorem]] states criteria for which those numberi ...s of strings as well. Given a sequence <math>x_1 x_2 x_3 ... x_n</math> of positive integers, the Gödel encoding is the product of the first n primes raised to ...

...jCNGuZ93z06kDmxXutGU8S_ADA6FgZw&cad=rja On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson], Ann. of. Math. '''39'''(1938), 350 * {{cite book | title=Prime Numbers: A Computational Perspective | author=Richard E. Crandall | coauthors=Carl ...

...something is true for all the [[natural numbers]] (all the positive whole numbers). The idea is that Prove that for all natural numbers ''n'': ...

is an algebraic equation over the rational numbers. ...s in the field of complex numbers. One can also look for solutions in real numbers. ...

...Much like hours on a [[clock]], which repeat every twelve hours, once the numbers reach a certain value, called the ''modulus'', they go back to zero. ...same [[remainder]] when both are [[division (mathematics)|divided]] by the positive integer ''n''. Congruence can be written this way: ...

...er above and to the right (if any) to find the new value. For example, the numbers 1 and 3 in the fourth row are added to make 4 in the fifth row. In general, when a binomial is raised to a positive integer power we have: ...

.../n</math>, the probability that <math>R</math> is good is larger than some positive constant. ...>p</math>, the probability that <math>R</math> is good is larger than some positive constant. <STRIKE>(Hint: Use the second moment.)</STRIKE> ...

...s is negative, and the sum of every <math>m</math> consecutive elements is positive. ...)\geq m+n-2</math>, for any <math>n,m</math> are relatively prime(the only positive integer factor that divides both of them is 1). ...

.../n</math>, the probability that <math>R</math> is good is larger than some positive constant. ...>p</math>, the probability that <math>R</math> is good is larger than some positive constant. ...

A [[number]] is called a '''perfect number''' if by adding all the positive [[divisor]]s of the number (except itself), the result is the number itself ...he number itself: 6) are 1, 2, and 3 and 1 + 2 + 3 equals 6. Other perfect numbers include 28, 496 and 8128. ...

...wo of the simplest infinite sets, that of [[natural number]]s, and that of positive [[fraction (mathematics)|fractions]]. The idea is to show that both of thes Next, the numbers are counted, as shown. Fractions which can be simplified are left out: ...

...point out the dot that is sometimes used to separate the positions of the numbers in this [[system]]. Almost everyone uses this nowadays and prefers the conv ...icates the start of a fractional part, and with one of the sign symbols + (positive) or − (negative) in front of the numerals to indicate sign. ...

...utions but you need to find the real solutions. Inequality is solving real numbers. The proper way to read inequality is from left to right, just like the oth ...A number line is one way to show the location relative to all other real numbers.<ref>{{Cite web|url=http://go.galegroup.com/ps/retrieve.do?sort=RELEVANCE&i ...

...ion is shifted down by one. This means that if n is a [[Sign_(mathematics)|positive]] [[integer]] The gamma function is defined for all [[complex numbers]]. But it is not defined for negative integers and zero. For a complex numb ...

A '''negative exponent''' is the reciprocal of a number with a positive exponent which can be mathematically represented as <math>x^{-1}=\frac{1}{x ...ent from -1. In this case the negative exponent can be separated from the positive exponent, so <math>x^{-2}=(x^{-1})^2=\left(\frac{1}{x}\right)^{2}=\frac{1} ...

...other other for +1. Each <math>c_i</math> gives the difference between the numbers of subjects with feature <math>i</math> in the two groups. By minimizing <m ...less than <math>\frac{k}{2}-\sqrt{2m\ln n}=\left(1-\delta\right)\mu</math> positive <math>b_i</math>'s, where <math>\delta=\frac{2\sqrt{2m\ln n}}{k}</math>. Ap ...

...ed a [[countable set]]. But if a set has the same cardinality as the real numbers, it is called an [[uncountable set]]. * <math>\mathbb{Z}</math>, denoting the set of all [[integer]]s (whether positive, negative or zero). So <math>\mathbb{Z}</math> = {..., -2, -1, 0, 1, 2, ... ...