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:For <math>n>0</math>, the numbers of subsets of an <math>n</math>-set of even and of odd cardinality are equa For counting problems, what we care about are ''numbers''. In the binomial theorem, a formal ''variable'' <math>x</math> is introdu ...

:For <math>n>0</math>, the numbers of subsets of an <math>n</math>-set of even and of odd cardinality are equa For counting problems, what we care about are ''numbers''. In the binomial theorem, a formal ''variable'' <math>x</math> is introdu ...

:For <math>n>0</math>, the numbers of subsets of an <math>n</math>-set of even and of odd cardinality are equa For counting problems, what we care about are ''numbers''. In the binomial theorem, a formal ''variable'' <math>x</math> is introdu ...

:For <math>n>0</math>, the numbers of subsets of an <math>n</math>-set of even and of odd cardinality are equa For counting problems, what we care about are ''numbers''. In the binomial theorem, a formal ''variable'' <math>x</math> is introdu ...

:For <math>n>0</math>, the numbers of subsets of an <math>n</math>-set of even and of odd cardinality are equa For counting problems, what we care about are ''numbers''. In the binomial theorem, a formal ''variable'' <math>x</math> is introdu ...

...input a set <math>S</math> of <math>n</math> numbers, we want to sort the numbers in <math>S</math> in increasing order. One of the most famous algorithm for ...re all numbers in <math>S_1</math> are smaller than <math>x</math> and all numbers in <math>S_2</math> are larger than <math>x</math>; ...

...v</sub> || E 2C₄ C₂ 2σ_v 2σ_d || square pyramidal || [[xenon oxytetrafluoride]] ...ub>'' ''i'' 2S₄ σ_h 2σ_v 2σ_d || square planar || [[xenon tetrafluoride]] ...

If there exists a '''[[square matrix]]''' called '''''A''''', a '''[[scalar]] ''λ''''', and a '''non-zero ...cation. For example, instead of [[real numbers]], scalars may be [[complex numbers]]; instead of arrows, vectors may be [[function (mathematics)|functions]] ...

Sampling <math>t</math> mutually independent random numbers from <math>[p]</math> can be quite expensive since it requires <math>\Omega The error is reduced to <math>1/t</math> with only two random numbers. This scheme works as long as <math>t\le p</math>. ...

Sampling <math>t</math> mutually independent random numbers from <math>[p]</math> can be quite expensive since it requires <math>\Omega The error is reduced to <math>1/t</math> with only two random numbers. This scheme works as long as <math>t\le p</math>. ...

...ximation ratio of 2 to being 2-universal. The proof uses the fact that odd numbers are relative prime to a power of 2. We exploit that C-multiplication (*) of unsigned u-bit numbers is done <math>\bmod 2^u</math>, and have a one-line C-code for computing th ...

...ximation ratio of 2 to being 2-universal. The proof uses the fact that odd numbers are relative prime to a power of 2. We exploit that C-multiplication (*) of unsigned u-bit numbers is done <math>\bmod 2^u</math>, and have a one-line C-code for computing th ...

Sampling <math>t</math> mutually independent random numbers from <math>[p]</math> can be quite expensive since it requires <math>\Omega The error is reduced to <math>1/t</math> with only two random numbers. This scheme works as long as <math>t\le p</math>. ...

<math>\square</math> ...to introduce the concepts of the <math>k</math>-cascade representation of numbers and the colex order of sets. ...

<math>\square</math> ...to introduce the concepts of the <math>k</math>-cascade representation of numbers and the colex order of sets. ...

...ted as a diagram of dots (or squares), called a '''Ferrers diagram''' (the square version of Ferrers diagram is also called a '''Young diagram''', named afte |align=center|Ferrers diagram (''square version'') of (5,4,2,1) ...

...re related. For a vector '''a''', the dot product '''a''' · '''a''' is the square of the length of '''a''', or Unlike multiplication of ordinary numbers, where if ''ab'' = ''ac'', then ''b'' always equals ''c'' unless ''a'' is z ...

...ximation ratio of 2 to being 2-universal. The proof uses the fact that odd numbers are relative prime to a power of 2. We exploit that C-multiplication (*) of unsigned u-bit numbers is done <math>\bmod 2^u</math>, and have a one-line C-code for computing th ...

...multiply amplitude by amplitude (or in other words he had to [[wikt:square|square]] the amplitude) to get the intensity he wanted. He had to figure out how t ...no problem. But they were both complicated equations, and how you got the numbers to plug into the equations turned out to be different depending on which wa ...

...nd therefore frequency). So the formula that Planck worked out to make the numbers all come out right was: Putting in different numbers for '''m''' and '''n''', it is easy to predict frequencies for many types o ...