Theorems · Theorem · number theory
Rat.AbsoluteValue.equiv_real_or_padic
- 1000+ list: Ostrowski's theorem
∀ (f : AbsoluteValue ℚ ℝ), f.IsNontrivial → f ≈ Rat.AbsoluteValue.real ∨ ∃! p, ∃ (x : Fact (Nat.Prime p)), f ≈ Rat.AbsoluteValue.padic p
Ostrowski's Theorem: every absolute value (with values in ℝ) on ℚ is equivalent
to either the standard absolute value or a p-adic absolute value for a prime p.
- Defined in
- Mathlib.NumberTheory.Ostrowski
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Factstatement · cited by 2,726
- Nat.Primestatement · cited by 2,059
- AbsoluteValuestatement and proof · cited by 363
- ExistsUniquestatement · cited by 268
- AbsoluteValue.IsNontrivialstatement and proof · cited by 17
- Rat.AbsoluteValue.padicstatement · cited by 6
- Rat.AbsoluteValue.realstatement · cited by 4
- Rat.AbsoluteValue.equiv_padic_of_boundedproof · cited by 1
- Rat.AbsoluteValue.equiv_real_of_unboundedproof · cited by 1
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