The positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.
- This means that the natural numbers, the integers, and the even integers all have the ‘same number’ of elements.
- In particular he showed that if any countable set has an arithmetic where the elements have unique decompositions into primes, then it is isomorphic to the arithmetic of the natural numbers.
- In contrast, Fermat had managed to show that you couldn't find natural numbers with a + b = c, using a method he called steepest descent.
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