Web Reference: Dec 14, 2025 · Both discrete and continuous variables generally do have changing values—and a discrete variable can vary continuously with time. I am quite aware that discrete variables are those values that you can count while continuous variables are those that you can measure such as weight or height. Nov 17, 2013 · @user1742188 It follows from Heine-Cantor Theorem, that a continuous function over a compact set (In the case of $\mathbb {R}$, compact sets are closed and bounded) is uniformly continuous. Jul 22, 2010 · The cardinality is at most that of the continuum because the set of real continuous functions injects into the sequence space $\mathbb R^N$ by mapping each continuous function to its values on all the rational points. Since the rational points are dense, this determines the function.
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