Theorems · Theorem · order theory
archimedean_iff_nat_lt
∀ {K : Type u_4} [inst : Field K] [inst_1 : LinearOrder K] [IsStrictOrderedRing K],
Archimedean K ↔ ∀ (x : K), ∃ n, x < ↑n- Defined in
- Mathlib.Algebra.Order.Archimedean.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsStrictOrderedRingstatement and proof · cited by 2,490
- le_of_ltproof · cited by 1,175
- Archimedeanstatement · cited by 603
- nsmul_eq_mulproof · cited by 369
- div_lt_iff₀proof · cited by 45
- exists_nat_gtproof · cited by 26
Cited by5
Results whose statement or proof uses this declaration.
- archimedean_iff_rat_ltproof · cited by 2
- tendsto_exp_div_rpow_atTopproof · cited by 1
- archimedean_iff_int_ltproof · cited by 1
- ConditionallyCompleteLinearOrderedField.to_archimedeanproof · cited by 0
- archimedean_iff_nat_leproof · cited by 0