Theorems · Theorem · logic and foundations
Hyperreal.infinitesimal_iff_infinite_inv
Deprecated since 2026-01-05Mathlib marks this declaration as deprecated.
∀ {x : ℝ*}, x ≠ 0 → (x.Infinitesimal ↔ x⁻¹.Infinite)- Defined in
- Mathlib.Analysis.Real.Hyperreal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- inv_invproof · cited by 494
- Hyperrealstatement and proof · cited by 172
- inv_ne_zeroproof · cited by 99
- Hyperreal.Infinitestatement · cited by 45
- Hyperreal.Infinitesimalstatement and proof · cited by 41
- Hyperreal.infinite_iff_infinitesimal_invproof · cited by 2
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