mathlib documentation

data.​rat.​floor

data.​rat.​floor

source
rat.​floor
rat.​floor_def
rat.​floor_ring
rat.​le_floor

Floor Function for Rational Numbers

Summary

We define the floor function and the floor_ring instance on ℚ.

Tags

rat, rationals, ℚ, floor

source
def rat.​floor  :
ℚ → ℤ

floor q is the largest integer z such that z ≤ q

Equations
source
theorem rat.​le_floor {z : ℤ} {r : ℚ} :
z ≤ r.floor ↔ ↑z ≤ r

source
@[instance]
def rat.​floor_ring  :
floor_ring ℚ

Equations
source
theorem rat.​floor_def {q : ℚ} :
⌊q⌋ = q.num / ↑(q.denom)

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