Theorems · Theorem · logic and foundations
Hyperreal.infinite_iff_infinitesimal_inv
Deprecated since 2026-01-05Mathlib marks this declaration as deprecated.
∀ {x : ℝ*}, x ≠ 0 → (x.Infinite ↔ x⁻¹.Infinitesimal)- Defined in
- Mathlib.Analysis.Real.Hyperreal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Hyperrealstatement and proof · cited by 172
- Hyperreal.Infinitestatement · cited by 45
- Hyperreal.Infinitesimalstatement · cited by 41
- Hyperreal.infinite_of_infinitesimal_invproof · cited by 1
- Hyperreal.infinitesimal_inv_of_infiniteproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Hyperreal.infinitesimal_iff_infinite_invproof · cited by 0
- Hyperreal.infinite_omegaproof · cited by 0