Theorems · Theorem · number theory
Rat.AbsoluteValue.equiv_real_of_unbounded
∀ {f : AbsoluteValue ℚ ℝ}, (¬∀ (n : ℕ), f ↑n ≤ 1) → f.IsEquiv Rat.AbsoluteValue.realIf f is not bounded and not trivial, then it is equivalent to the standard absolute value on
ℚ.
- Defined in
- Mathlib.NumberTheory.Ostrowski
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- LT.lt.ne'proof · cited by 1,417
- le_of_ltproof · cited by 1,175
- zero_lt_oneproof · cited by 598
- lt_of_not_geproof · cited by 374
- LT.lt.transproof · cited by 370
- AbsoluteValuestatement and proof · cited by 363
- CharP.cast_eq_zeroproof · cited by 357
- Nat.cast_pos'proof · cited by 219
Cited by1
Results whose statement or proof uses this declaration.
- Rat.AbsoluteValue.equiv_real_or_padicproof · cited by 0