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The blow-up lemma essentially says that regular pairs in Szemerédi's regularity lemma behave like complete bipartite graphs from the point of view of embedding bounded degree ...

Let r and s be positive integers which are relatively prime and let a and b be any two integers. Then there is an integer N such that N=a (mod r) (1) and N=b (mod s). (2) ...

In geometry, an endpoint is one of the two points at the boundary of a line segment. In analysis, an endpoint is one of the two points at the boundary of a closed interval or ...

For a permutation alpha in the symmetric group S_p, the alpha-permutation graph of a labeled graph G is the graph union of two disjoint copies of G (say, G_1 and G_2), ...

One of the numbers 1, 2, 3, ... (OEIS A000027), also called the counting numbers or natural numbers. 0 is sometimes included in the list of "whole" numbers (Bourbaki 1968, ...

The exists quantifier exists .

If the average number of envelopes per pigeonhole is a, then some pigeonhole will have at least a envelopes. Similarly, there must be a pigeonhole with at most a envelopes.

Infinity, most often denoted as infty, is an unbounded quantity that is greater than every real number. The symbol infty had been used as an alternative to M (1000) in Roman ...

An operator in logic which returns either true or false.

((a+b)/2)^2-((a-b)/2)^2=ab.