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The positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.
- ‘Cantor proves that the algebraic real numbers are in one-one correspondence with the natural numbers in the following way.’
- ‘This means that the natural numbers, the integers, and the even integers all have the ‘same number’ of elements.’
- ‘In 1889 Peano published his famous axioms, called Peano axioms, which defined the natural numbers in terms of sets.’
- ‘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.’
- ‘For what they thought they had done was establish a deep result about how the primes are distributed among 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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