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