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What is an integer?

What is an integer? Here are some definitions.

Noun
  1. (arithmetic) A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3,...}.
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In the 1980s, personal computers, for example, often contained separate processors for floating-point operations and integer operations.
A transcendental number is an irrational number that is not a root of any polynomial equation with integer coefficients.
The point groups of the remaining 7 crystal classes can not be described by orthogonal integer matrices.
In it Vinogradov proved that every sufficiently large odd integer can be expressed as the sum of three primes.
Generalizing the Pythagorean equation for triangles with integer sides to powers greater than 2 leads to Fermat's last theorem.
When writing an integer in decimal we use, essentially, a units column, a tens column, a hundreds column, a thousands column, and so on.

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