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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.
The floor function rounds down by taking a non-integer value to the next integer below it.
The function produces the smallest integer that's greater than the given number.
The point groups of the remaining 7 crystal classes can not be described by orthogonal integer matrices.
Generalizing the Pythagorean equation for triangles with integer sides to powers greater than 2 leads to Fermat's last theorem.
A transcendental number is an irrational number that is not a root of any polynomial equation with integer coefficients.

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