Uncountable Meagre Sets Besides The Cantor Set

[onemachine]

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!

[onemachine]

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.

[onemachine]

I don't get it...everyone runs around claiming there exist all these dense meagre sets but no one can show one exists...

[onemachine]

I have explicitly defined a first category set that is dense AND nowhere dense in the entire real line. Thanks for the help [sarcasm]