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Let P be a polynomial of degree n with derivative P^'. Then ||P^'||_infty<=n||P||_infty, where ||P||_infty=max_(|z|=1)|P(z)|.

(1) Based on or involving trial and error. (2) Convincing without being rigorous.

A polynomial x^n+a_(n-1)x^(n-1)+...+a_1x+a_0 in which the coefficient of the highest order term is 1.

A graph is said to be regular of degree r if all local degrees are the same number r. A 0-regular graph is an empty graph, a 1-regular graph consists of disconnected edges, ...

A number n for which a shortest chain exists which is a Brauer chain is called a Brauer number. There are infinitely many non-Brauer numbers.

The cardinal number of any set is lower than the cardinal number of the set of all its subsets. A corollary is that there is no highest aleph (aleph).

The logarithm of the reciprocal of a number, equal to the negative of the logarithm of the number itself, cologx=log(1/x)=-logx.

A complex translation is a map of the form z|->z+a, where a is a fixed complex number, which corresponds to translation (shifting) of points the complex plane by the complex ...

A number which can be computed to any number of digits desired by a Turing machine. Surprisingly, most irrationals are not computable numbers!

The area of a rational right triangle cannot be a square number. This statement is equivalent to "a congruum cannot be a square number."