Abstract
AbstractWe write for the cardinality of the set of finite sequences of a set which is of cardinality . With the Axiom of Choice (), for every infinite cardinal where is the cardinality of the permutations on a set which is of cardinality . In this paper, we show that “ for every cardinal ” is provable in and this is the best possible result in the absence of . Similar results are also obtained for : the cardinality of the set of finite sequences without repetition of a set which is of cardinality .
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