Theorems · Theorem · logic and foundations
Hyperreal.infinite_iff_abs_lt_abs
Deprecated since 2026-01-05Mathlib marks this declaration as deprecated.
∀ {x : ℝ*}, x.Infinite ↔ ∀ (r : ℝ), |↑r| < |x|- Defined in
- Mathlib.Analysis.Real.Hyperreal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- absstatement and proof · cited by 1,814
- LE.le.trans_ltproof · cited by 795
- Hyperrealstatement and proof · cited by 172
- le_abs_selfproof · cited by 113
- Hyperreal.ofRealstatement and proof · cited by 68
- Hyperreal.Infinitestatement · cited by 45
- Hyperreal.InfinitePosproof · cited by 44
- Hyperreal.coe_absproof · cited by 2
- Hyperreal.infinitePos_abs_iff_infiniteproof · cited by 1
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