The quality or state of being compact; density, tightness, or conciseness; the degree to which something occupies minimal space.
From 'compact' + '-ness' (abstract noun suffix). This noun has been used since Middle English to describe the abstract quality of being compact or condensed.
In mathematics, compactness is a transformative concept: a compact space is so perfectly self-contained that every infinite sequence has a convergence point—it's why compactness is fundamental to proving that calculus actually works the way we think it does.
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