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Aug 17, 2013 at 11:31 comment added Joel David Hamkins You're welcome (although my name is Hamkins). For $K$ larger than the continuum, it will often happen that $|K^{\mathbb{N}}|=|K|$ (but definitely not always), which may make things easier to think about.
Aug 17, 2013 at 11:17 comment added user38700 Many thanks Mr Hampkins for your generous answer. I still need to know if the answer is always the optimal one, namely $|K|^{\aleph_0}$, where $|K|$ denotes the cardinality of $K$. If anybody knows the answer, I would be grateful.
Aug 17, 2013 at 0:09 history edited Joel David Hamkins CC BY-SA 3.0
Improved exposition
Aug 16, 2013 at 22:11 history edited Joel David Hamkins CC BY-SA 3.0
Simplified the argument, handle K up to size continuum
Aug 16, 2013 at 18:53 history edited Joel David Hamkins CC BY-SA 3.0
added 305 characters in body
Aug 16, 2013 at 18:46 history answered Joel David Hamkins CC BY-SA 3.0