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For any two integers a and b, suppose d|ab. Then if d is relatively prime to a, then d divides b. This results appeared in Euclid's Elements, Book VII, Proposition 30. This ...

A Jordan algebra which is not isomorphic to a subalgebra.

Expansion is an affine transformation (sometimes called an enlargement or dilation) in which the scale is increased. It is the opposite of a geometric contraction, and is ...

Exponentiation is the process of taking a quantity b (the base) to the power of another quantity e (the exponent). This operation most commonly denoted b^e. In TeX, the ...

An (n-1)-dimensional face of an n-dimensional polytope. A procedure for generating facets is known as faceting.

A statement which is rigorously not true. Regular two-valued logic allows statements to be only true or false, but fuzzy logic treats "truth" as a continuum which can have a ...

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

The field axioms are generally written in additive and multiplicative pairs. name addition multiplication associativity (a+b)+c=a+(b+c) (ab)c=a(bc) commutativity a+b=b+a ...

The ring of fractions of an integral domain. The field of fractions of the ring of integers Z is the rational field Q, and the field of fractions of the polynomial ring ...

The field of rationals is the set of rational numbers, which form a field. This field is commonly denoted Q (doublestruck Q).