Theorems · Definition · real analysis
Function.Periodic
{α : Type u_1} → {β : Type u_2} → [Add α] → (α → β) → α → PropA function f is said to be Periodic with period c if for all x, f (x + c) = f x.
- Defined in
- Mathlib.Algebra.Ring.Periodic
- Cited by
- 154 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 8 definitions · uses no axioms
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by155
Results whose statement or proof uses this declaration.
- Function.Periodic.int_mulstatement and proof · cited by 18
- Real.cos_periodicstatement · cited by 16
- Function.Periodic.nat_mulstatement and proof · cited by 15
- Complex.cos_periodicstatement · cited by 15
- Real.tan_periodicstatement · cited by 14
- Function.Periodic.sub_eqstatement and proof · cited by 13
- Function.Periodic.eqstatement and proof · cited by 12
- Complex.tan_periodicstatement · cited by 11
- SlashInvariantFormClass.periodic_comp_ofComplexstatement · cited by 11
- Function.Antiperiodic.periodic_two_mulstatement · cited by 10
- Real.sin_periodicstatement · cited by 10
- Function.Periodic.nsmulstatement and proof · cited by 9