Theorems · Theorem · number theory
irrational_iff_ne_rational
∀ (x : ℝ), Irrational x ↔ ∀ (a b : ℤ), b ≠ 0 → x ≠ ↑a / ↑b
- Defined in
- Mathlib.NumberTheory.Real.Irrational
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Irrationalstatement · cited by 139
- Rat.cast_intCastproof · cited by 74
- Rat.cast_divproof · cited by 37
Cited by1
Results whose statement or proof uses this declaration.
- Real.infinite_rat_abs_sub_lt_one_div_den_sq_iff_irrationalproof · cited by 0