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BGW.Probability.NNReal

Rational approximation in nonnegative reals #

This module records the density of nonnegative rationals in ℝ≥0 in the form used for countable rational approximations of real-valued constructions.

theorem BGW.Probability.exists_nnrat_btwn {a b : NNReal} (h : a < b) :
∃ (q : ℚ≥0), a < ↑q ∧ ↑q < b

Every strict inequality between nonnegative reals has a nonnegative rational strictly between its endpoints.