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ℝ: rationals, irrationals, approximations, decreasing geometric progression

The set of real numbers
All numbers studied in school as one system are called real; their set is denoted R\mathbb{R}. Think of it as the number line: it marks both rational and irrational points, and between any two reals there are more reals.
QR\mathbb{Q}\subset\mathbb{R} — rationals lie inside the reals but do not exhaust them
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