Peano arithmetic: Difference between revisions
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Peano arithmetic is a first-order axiomatization of the theory of the [[natural numbers]] introduced by Giuseppe. It is a system of arithmetic which includes basic rules of nonnegative arithmetic - transitivity, symmetry and reflexivity of equality, the definitions of addition and multiplication, nonexistence of -1 (i.e. a number whose successor is zero), injectivity of the successor operation, and the induction schema. The induction schema gives Peano arithmetic the bulk of its power, and enables it to prove virtually all number-theoretic theorems.<ref>Mendelson, Elliott (December 1997) [December 1979]. ''Introduction to Mathematical Logic (Discrete Mathematics and Its Applications)'' (4th ed.). Springer.</ref> |
Peano arithmetic is a first-order axiomatization of the theory of the [[natural numbers]] introduced by Giuseppe. It is a system of arithmetic which includes basic rules of nonnegative arithmetic - transitivity, symmetry and reflexivity of equality, the definitions of addition and multiplication, nonexistence of -1 (i.e. a number whose successor is zero), injectivity of the successor operation, and the induction schema. The induction schema gives Peano arithmetic the bulk of its power, and enables it to prove virtually all number-theoretic theorems.<ref>Mendelson, Elliott (December 1997) [December 1979]. ''Introduction to Mathematical Logic (Discrete Mathematics and Its Applications)'' (4th ed.). Springer.</ref> |
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