Theorems · Definition · real analysis
OrderEmbedding.sigmoid
ℝ ↪o ↑unitInterval
The Sigmoid function as an OrderEmbedding from ℝ to I.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 156 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.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Set.Elemstatement · cited by 7,166
- OrderEmbeddingstatement · cited by 619
- unitIntervalstatement · cited by 607
- unitInterval.sigmoidproof · cited by 19
- OrderEmbedding.ofStrictMonoproof · cited by 15
- unitInterval.sigmoid_strictMonoproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Topology.isEmbedding_sigmoidproof · cited by 1