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It is well known that the

The cardinality of the set of all root paths in the infinite complete binary tree is equal to the cardinality of the Continuum. The same holds true for k-ary trees for any finite k. But what is the case for k infinite?

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It is well known that the cardinality of the set of all paths in the infinite complete binary tree is equal to the cardinality of the Continuum. The same holds true for n-ary k-ary trees for any finite nk. But what is the case when n tends towards infinityfor k infinite?

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