Theorems · Definition · logic and foundations
Hyperreal.Infinitesimal
Deprecated since 2026-01-05Use ArchimedeanClass.mk instead.
ℝ* → Prop
A hyperreal number is infinitesimal if its standard part is 0.
Do not use. Write 0 < ArchimedeanClass.mk x instead.
- Defined in
- Mathlib.Analysis.Real.Hyperreal
- Cited by
- 41 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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.IsStproof · cited by 42
Cited by41
Results whose statement or proof uses this declaration.
- Hyperreal.infinitePos_mul_of_infinitePos_not_infinitesimal_posstatement and proof · cited by 6
- Hyperreal.infinitePos_iff_infinitesimal_inv_posstatement and proof · cited by 5
- Hyperreal.infinitesimal_defstatement · cited by 5
- Hyperreal.Infinite.not_infinitesimalstatement and proof · cited by 3
- Hyperreal.infiniteNeg_iff_infinitesimal_inv_negstatement and proof · cited by 3
- Hyperreal.infiniteNeg_mul_of_infiniteNeg_not_infinitesimal_posstatement and proof · cited by 3
- Hyperreal.infiniteNeg_mul_of_infinitePos_not_infinitesimal_negstatement and proof · cited by 3
- Hyperreal.infinitePos_mul_of_infiniteNeg_not_infinitesimal_negstatement and proof · cited by 3
- Hyperreal.infinitesimal_negstatement and proof · cited by 3
- Hyperreal.InfiniteNeg.not_infinitesimalstatement · cited by 2
- Hyperreal.InfinitePos.not_infinitesimalstatement · cited by 2
- Hyperreal.infinite_iff_infinitesimal_invstatement · cited by 2