Theorems · Theorem · information theory
Real.binEntropy_neg_of_neg
∀ {p : ℝ}, p < 0 → Real.binEntropy p < 0Outside the usual range of binEntropy, it is negative. This is due to log p = log |p|.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- Real.logproof · cited by 939
- le_of_not_gtproof · cited by 430
- lt_of_not_geproof · cited by 374
- neg_neg_of_posproof · cited by 227
- Real.log_oneproof · cited by 91
- Real.log_posproof · cited by 51
- mul_pos_of_neg_of_negproof · cited by 40
- Real.log_invproof · cited by 35
Cited by4
Results whose statement or proof uses this declaration.
- Real.binEntropy_nonpos_of_nonposproof · cited by 3
- Real.binEntropy_neg_of_one_ltproof · cited by 1
- Real.binEntropy_eq_zeroproof · cited by 0
- Real.qaryEntropy_neg_of_negproof · cited by 0