Theorems · Definition · real analysis
Real.sqrt
ℝ → ℝ
The square root of a real number. This returns 0 for negative inputs.
This has notation √x. Note that √x⁻¹ is parsed as √(x⁻¹).
- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 545 results in Mathlib
- Foundations
- Depth 125 from the axioms, rests on 3,457 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NNReal.toRealproof · cited by 1,260
- Real.toNNRealproof · cited by 267
- NNReal.sqrtproof · cited by 91
Cited by578
Results whose statement or proof uses this declaration.
- Complex.norm_realproof · cited by 105
- Complex.norm_mulproof · cited by 59
- Real.arsinhproof · cited by 55
- Real.sq_sqrtstatement and proof · cited by 53
- Real.sqrt_pos_of_posstatement · cited by 50
- Complex.norm_Iproof · cited by 46
- Real.sqrt_sqstatement and proof · cited by 36
- Real.sqrt_nonnegstatement · cited by 35
- Real.sqrt_mulstatement · cited by 32
- Real.sqrt_zerostatement · cited by 28
- Real.arcoshproof · cited by 27
- Real.goldenRatioproof · cited by 25
Showing the 200 most cited of 578.