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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 1889 Peano published his famous axioms, called Peano axioms, which defined the natural numbers in terms of sets.’
‘Cantor proves that the algebraic real numbers are in one-one correspondence with the natural numbers in the following way.’
‘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.’
‘For what they thought they had done was establish a deep result about how the primes are distributed among the natural numbers.’