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A proof of a formula on limits based on the epsilon-delta definition. An example is the following proof that every linear function f(x)=ax+b (a,b in R,a!=0) is continuous at ...

The conjecture that Frey's elliptic curve was not modular. The conjecture was quickly proved by Ribet (Ribet's theorem) in 1986, and was an important step in the proof of ...

An equation is a mathematical expression stating that two or more quantities are the same as one another, also called an equality, formula, or identity.

There are two similar but distinct concepts related to equidecomposability: "equidecomposable" and "equidecomposable by dissection." The difference is in that the pieces ...

Parallel lines are everywhere equidistant. This postulate is equivalent to the parallel postulate.

Let A and B be two classes of positive integers. Let A(n) be the number of integers in A which are less than or equal to n, and let B(n) be the number of integers in B which ...

A curve in two dimensions on which the value of a function f(x,y) is a constant. Other synonymous terms are isarithm, isopleth, and contour line. A plot of several ...

A distribution of error such that the error remaining is always given approximately by the last term dropped.

Two matrices A and B are equal to each other, written A=B, if they have the same dimensions m×n and the same elements a_(ij)=b_(ij) for i=1, ..., n and j=1, ..., m. ...

Suppose a,b in N, n=ab+1, and x_1, ..., x_n is a sequence of n real numbers. Then this sequence contains a monotonic increasing (decreasing) subsequence of a+1 terms or a ...