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Normal [[hotel]]s have a set number of rooms. This number is [[finite]]. Once every room has been assigned to a guest, any new guest ...s already full, something that could not happen in any hotel with a finite number of rooms. ...

...ne by the Babylonians; Ancient Greeks, like [[Ptolemy]] later extended the theory. The third number is the height, altitude, or depth. This is given with respect to some fixed ...

A '''square number''', sometimes also called a '''perfect square''', is the result of an [[int ...exponentiation]]), usually pronounced as "''n'' squared". The name square number comes from the name of the shape; see [[#Properties|below]]. ...

...ord.</ref>^p160 It is a central idea in [[evolution|evolutionary theory]]. Fitness is usually equal to the proportion of the individual's [[gene]]s ...or to help relatives with similar genes to reproduce, ''as long as similar number of copies of individual's genes get passed on to the next generation''. Sel ...

...ers rolls a (fair) 6-sided die. For any pair of players who throw the same number, the group scores <math>1</math> point. Find the mean and variance of the t == Problem 3 (Probability meets graph theory) == ...

...on]] within a hydrogen atom can only be [[integer]] multiples of a certain number. ...ful because it explains the cause of [[light]]. Bohr agreed with classical theory that light has a wave-particle duality (meaning that it is made of both [[e ...

The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one ...\mathbb{R}</math> is a function that maps each event to a nonnegative real number, satisfying ...

:''This article is about the basic notions. For advanced topics, see [[Group theory]].'' The number of elements in a group is called the group's ''order''. ...

...the positive [[divisor]]s of the number (except itself), the result is the number itself. 6 is the first perfect number. Its divisors (other than the number itself: 6) are 1, 2, and 3 and 1 + 2 + 3 equals 6. Other perfect numbers in ...

...ow that a [[mathematics|math]] [[theorem]] is true. One must show that the theory is true in all cases. ...lways true, precisely because it's true for whatever comes after any given number. ...

Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can We consider a typical extremal problem for graphs: the largest possible number of edges of '''triangle-free''' graphs, i.e. graphs contains no <math>K_3</ ...

Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can We consider a typical extremal problem for graphs: the largest possible number of edges of '''triangle-free''' graphs, i.e. graphs contains no <math>K_3</ ...

Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can We consider a typical extremal problem for graphs: the largest possible number of edges of '''triangle-free''' graphs, i.e. graphs contains no <math>K_3</ ...

Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can We consider a typical extremal problem for graphs: the largest possible number of edges of '''triangle-free''' graphs, i.e. graphs contains no <math>K_3</ ...

Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can We consider a typical extremal problem for graphs: the largest possible number of edges of '''triangle-free''' graphs, i.e. graphs contains no <math>K_3</ ...

== Extremal Graph Theory == Extremal grap theory studies the problems like "how many edges that a graph <math>G</math> can ...

...th> players rolls a (fair) die. For any pair of players who throw the same number, the group scores <math>1</math> point. Find the mean and variance of the t == Problem 3 (Probability meets graph theory) == ...

Extremal graph theory studies the problems like "how many edges that a graph <math>G</math> can We consider a typical extremal problem for graphs: the largest possible number of edges of '''triangle-free''' graphs, i.e. graphs contains no <math>K_3</ ...

The axiom foundation of probability theory is laid by [http://en.wikipedia.org/wiki/Andrey_Kolmogorov Kolmogorov], one ...\mathbb{R}</math> is a function that maps each event to a nonnegative real number, satisfying ...

<li>[<strong>Random number of random variables</strong>] Let <math>\{X_n\}_{n \ge 1}</math> be identic ...rom the <strong>second</strong> round of tosses, and <math>Y</math> be the number of heads resulting from <strong>all</strong> tosses, which includes the fir ...