Theorems · Definition · real analysis
Real.sign
ℝ → ℝ
The sign function that maps negative real numbers to -1, positive numbers to 1, and 0 otherwise.
- Defined in
- Mathlib.Data.Real.Sign
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by13
Results whose statement or proof uses this declaration.
- Real.sign_of_posstatement · cited by 8
- Real.sign_of_negstatement · cited by 7
- Real.sign_zerostatement · cited by 5
- Real.sign_apply_eqstatement · cited by 1
- Real.sign_eq_zero_iffstatement and proof · cited by 1
- Real.sign_mul_nonnegstatement and proof · cited by 1
- Real.sign_apply_eq_of_ne_zerostatement · cited by 0
- Real.sign_intCaststatement and proof · cited by 0
- Real.sign_invstatement and proof · cited by 0
- Real.sign_mul_pos_of_ne_zerostatement and proof · cited by 0
- Real.inv_signstatement and proof · cited by 0
- Real.sign_negstatement and proof · cited by 0