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WebDefinition 8.1.1 (Countable sets) A set X is said to be countably infinite ( or just countable ) iff it has equal cardinality with the natural numbers \mathbf {N} . A set X is said to be at most countable iff it is either countable or finite . We say that a set is uncountable if it is infinite but not countable . Web12 nov. 2011 · How to prove for every open cover of the real numbers $\mathbb{R}$ there is a countable subcover? Without using more sophisticated results from topology, assuming only a real analysis background. ... Stack Exchange Network. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, ... fun things couples can do together at home
Every open cover of the real numbers has a countable subcover …
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