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The doublestruck capital letter Z, Z, denotes the ring of integers ..., -2, -1, 0, 1, 2, .... The symbol derives from the German word Zahl, meaning "number" (Dummit and Foote ...

The identity element of an additive monoid or group or of any other algebraic structure (e.g., ring, module, abstract vector space, algebra) equipped with an addition. It is ...

Every even number is the difference of two consecutive primes in infinitely many ways (Dickson 2005, p. 424). If true, taking the difference 2, this conjecture implies that ...

In the usual diagram of inclusion homomorphisms, if the upper two maps are injective, then so are the other two. More formally, consider a space X which is expressible as the ...

A dozen dozen, also called a gross. 144 is a square number and a sum-product number.

The digits in the number 2187 form the two vampire numbers: 21×87=1827 and 2187=27×81. 2187 is also given by 3^7.

The number 24 is equal to 4! (four factorial). A number puzzle asks to construct 24 in as many ways possible using elementary mathematical operations on three copies of the ...

A generalization of the Lebesgue integral. A measurable function f(x) is called A-integrable over the closed interval [a,b] if m{x:|f(x)|>n}=O(n^(-1)), (1) where m is the ...

By way of analogy with the eban numbers, aban numbers are defined as numbers whose English names do not contain the letter "a" (i.e., "a" is banned). Note that this ...

A group or other algebraic object is said to be Abelian (sometimes written in lower case, i.e., "abelian") if the law of commutativity always holds. The term is named after ...