Uncountable Meagre Sets Besides The Cantor Set

onemachine

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Feb 2, 2012
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I would like to define an uncountable meagre set that is dense in the real line such that the Cantor set is not a subset of my set.

Any ideas? Thanks!
 
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Does my bank account qualify? It certainly gives every impression of being uncountably and depressingly meagre. ;)

Unfortunately, your bank account is not dense in any interval. So no, your bank account does not qualify.
 
I don't get it...everyone runs around claiming there exist all these dense meagre sets but no one can show one exists...
 
I have explicitly defined a first category set that is dense AND nowhere dense in the entire real line. Thanks for the help [sarcasm]
 
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