2023-04-21 13:17:21 +00:00
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import Bookshelf.Real.Basic
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2023-05-02 17:29:42 +00:00
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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) := x ∉ Set.range RatCast.ratCast
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2023-04-21 13:17:21 +00:00
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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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2023-04-22 19:11:50 +00:00
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of `ℚ` expect this (by proving the numerator and denominator are co-prime).
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2023-04-21 13:17:21 +00:00
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-/
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2023-05-02 17:29:42 +00:00
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def rational (x : ℝ) := ¬ irrational x
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