25 is an integer

Whole numbers

The whole numbersZ - considered as a subset of the real numbers - are an extension of the natural numbers. With the natural numbers we add their negative ones:

Z = N∪ {−n∣n∈N}.

In the area of ​​whole numbers, addition and subtraction can be carried out without restriction.

They form a ring.

Kit 5729A

For every subset of the whole numbers whose infimum (supremum) exists, it is also a minimum (maximum).

proof

Let M⊆Z and m = infM. We assume that m is not a minimum of M, so m∈ / M. But then m

The proof is carried out analogously for supremum / maximum. □

It is impossible to adequately convey the beauties of the laws of nature if one does not understand math. I regret that, but I guess it is.

Richard Feynman

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