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These primitive propositions … suffice to deduce all the properties of the numbers that we shall meet in the sequel. There is, however, an infinity o… - Giuseppe Peano
" "These primitive propositions … suffice to deduce all the properties of the numbers that we shall meet in the sequel. There is, however, an infinity of systems which satisfy the five primitive propositions. … All systems which satisfy the five primitive propositions are in one-to-one correspondence with the natural numbers. The natural numbers are what one obtains by abstraction from all these systems; in other words, the natural numbers are the system which has all the properties and only those properties listed in the five primitive propositions
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About Giuseppe Peano
Giuseppe Peano (27 August 1858 – 20 April 1932) was an Italian mathematician, logician, and one of the founders of modern mathematical logic and set theory. His work, summarized in Formulario mathematico (1895) was highly influential and the standard Peano axioms of the natural numbers are named in his honor.
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Additional quotes by Giuseppe Peano
1. 0 is a number. 2. The immediate successor of a number is also a number. 3. 0 is not the immediate successor of any number. 4. No two numbers have the same immediate successor. 5. Any property belonging to 0 and to the immediate successor of any number that also has that property belongs to all numbers.
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