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Theorems · Theorem · real analysis

Function.Odd.map_zero

∀ {α : Type u_3} {β : Type u_4} [inst : AddCommGroup β] [IsAddTorsionFree β] {f : α → β} [inst_2 : NegZeroClass α],
  Function.Odd f → f 0 = 0

An odd function vanishes at zero.

Defined in
Mathlib.Algebra.Group.EvenFunction
Cited by
1 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupIsAddTorsionFreeNegZeroClass
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ZMod.completedLFunction_one_sub_odd · cited by 1ZMod.completedLFunction_o…AddCommGroup · cited by 12871AddCommGroupneg_zero · cited by 542neg_zeroIsAddTorsionFree · cited by 155IsAddTorsionFreeFunction.Odd · cited by 38Function.OddNegZeroClass · cited by 23NegZeroClassOdd.map_zeroCITED BYCITES

Cites5

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Cited by1

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