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1 - 1 is a number
2 - The immediate successor of a number also is a number.
3 - 1 is not the immediate successor of any number.
4 - Two different numbers are not as immediate successor.
5 -All property belonging to 1 and the immediate successor of any number that also have that property belongs to all numbers
( mathematical induction).
Peano axioms or postulates of Peano accurately define the set of natural numbers. Were established by the Italian mathematician Giuseppe Peano (1858-1932) in 1889.
Although Richard Dedekind tried to base the natural numbers, based on the ideas of set theory developed by this time that George Cantor, it was not Giuseppe Peano who provided an axiomatic definition of the set of natural numbers. He did this by five axioms, using three primitive concepts, Zero , number (natural number or negative integer) and the binary relation be successor (or next )
A axiom in philosophy, is an "obvious truth" that no requires proof, as is admitted by all, and on which to build the rest of knowledge, though, not all epistemologists agree with this definition "classic."
In mathematics, an axiom is not necessarily a truism, but a logical expression used in a deduction to arrive at a conclusion. In mathematics there are two types of axioms: logical axioms and non-logical axioms.
The word comes from the Greek axiom αξιωμα (axiom), which means "it seems fair" or what is considered obvious and without demonstration. The word comes from the Greek αξιοειν (axioein) which means "value", which in turn comes from αξιος (Axios) meaning "valuable" or "worthy." Among the ancient Greek philosophers an axiom was what appeared to be true without any need for proof.
Although Richard Dedekind tried to base the natural numbers, based on the ideas of set theory developed by this time that George Cantor, it was not Giuseppe Peano who provided an axiomatic definition of the set of natural numbers. He did this by five axioms, using three primitive concepts, Zero , number (natural number or negative integer) and the binary relation be successor (or next )
A axiom in philosophy, is an "obvious truth" that no requires proof, as is admitted by all, and on which to build the rest of knowledge, though, not all epistemologists agree with this definition "classic."
In mathematics, an axiom is not necessarily a truism, but a logical expression used in a deduction to arrive at a conclusion. In mathematics there are two types of axioms: logical axioms and non-logical axioms.
The word comes from the Greek axiom αξιωμα (axiom), which means "it seems fair" or what is considered obvious and without demonstration. The word comes from the Greek αξιοειν (axioein) which means "value", which in turn comes from αξιος (Axios) meaning "valuable" or "worthy." Among the ancient Greek philosophers an axiom was what appeared to be true without any need for proof.
Photos: GM
Source.: Wikipedia
Source.: Wikipedia
* This is an old post, to republish, to extend certain concepts, and mainly for the pleasure of re- share.
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