Theorems · Theorem · group theory
orderOf_zero
∀ (M₀ : Type u_6) [inst : MonoidWithZero M₀] [Nontrivial M₀], orderOf 0 = 0
In a nontrivial monoid with zero, the order of the zero element is zero.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidWithZeroNontrivial
Around this declaration
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nontrivialstatement and proof · cited by 2,416
- MonoidWithZerostatement and proof · cited by 456
- zero_powproof · cited by 361
- orderOfstatement · cited by 324
- isOfFinOrder_iff_pow_eq_oneproof · cited by 27
- orderOf_eq_zero_iffproof · cited by 8
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