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Diff — Natural number

Revision #1422 → #2825 · back to history

addedOne-to-one correspondence (bijection)2152f6afb065
addedWell-ordered setfa24131deb00
modifiedPositive integers and non-negative integers4008894646cc
FieldFrom #1422To #2825
mathlib.moduleMathlib.Data.PNat.DefsMathlib.Data.PNat.Notation
modifiedPeano axioms66ff56e95c78
FieldFrom #1422To #2825
mathlib.declNat.recNat.recAux
mathlib.moduleInit.Data.Nat.Basic
note`Nat` satisfies the Peano axioms (zero, injective successor, recursor `Nat.rec`), but Mathlib has no single bundled `PeanoAxioms` structure.`Nat` satisfies the Peano axioms (zero, injective successor, recursor `Nat.recAux`), but Mathlib has no single bundled `PeanoAxioms` structure.
addedInjectivity of successorc1061d6fe412
addedZero is not a successor0cf859019978
modifiedAxiom of induction247dd6470b21
FieldFrom #1422To #2825
mathlib.declNat.recNat.recAux
mathlib.moduleInit.Data.Nat.Basic
noteThe induction/recursion principle `Nat.rec` is the core recursor, with variants like `Nat.le_induction` and `Nat.strong_induction_on` in Mathlib.The induction/recursion principle `Nat.recAux` is the core recursor, with variants like `Nat.le_induction` and `Nat.strong_induction_on` in Mathlib.
addedAxiom of infinityaeff3a8ddbf8
addedCharacterization of ≤ via existence of c with a + c = b29053a57c462