Is there a proof that, say, the number represented by taking the decimal expansion of pi and removing all of the 3's, is still irrational?
(It's relatively easy to construct an irrational number that is rational if you remove all the 3's, so it's at least a nontrivial question. I think!)
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Or how many digits would you need to remove to make it rational? If you removed all the digits except "1", then it would be rational. But could you make it rational by only removing, say, 7 digits, or 5 digits. And would it matter which digits you remove?
@Pat
Ooh, excellent questions!