14 lines
396 B
Plaintext
14 lines
396 B
Plaintext
|
import Bookshelf.Real.Basic
|
|||
|
|
|||
|
/--
|
|||
|
Assert that a real number is rational.
|
|||
|
|
|||
|
Note this does *not* require the found rational to be in reduced form. Members
|
|||
|
of `ℚ` expect this (by proving the numerator and denominator are coprime).
|
|||
|
-/
|
|||
|
def rational (x : ℝ) := ∃ a : ℤ, ∃ b : ℕ, b ≠ 0 ∧ x = a / b
|
|||
|
|
|||
|
/--
|
|||
|
Assert that a real number is irrational.
|
|||
|
-/
|
|||
|
def irrational (x : ℝ) := ¬ rational x
|