In [[real analysis]], a branbranch of mathematics, '''Cantor's intersection theorem''', named after [[Georg Cantor]], is a theorem related to [[compact set]]s in '''R''', the set of [[real number]]s. It states that a decreasing nested [[sequence]] of non-empty, [[closed set|closed]] and [[bounded set|bounded]] subsets of '''R''' has nonempty intersection. In other words, supposing {''C''<sub>''k''</sub>} is a sequence of non-empty, closed and bounded sets satisfying
