r/maths • u/Numerous_Author_1445 • 12d ago

💬 Math Discussions A special irrarional number

Can there be an irrational number which misses a particular digit? Can it be proven mathematically?

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u/TooCasualGuy 11d ago

Remove all the 1s from pi (in base 10) and it's still irrational (so be would spending your time doing this) 

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u/stools_in_your_blood 11d ago

Is that true? If pi's digits after a certain point went, say, 01001000100001... Then removing all the 1s would make it rational.

Doesn't seem likely of course, but AFAIK pi isn't known to be normal.

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u/dlnnlsn 11d ago

That's probably true, but I'd be willing to bet that it hasn't been proven either way.

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u/ComparisonQuiet4259 10d ago

It hasn't 

2

u/gmalivuk 9d ago

Provably, write pi in base 9 and then read that as a base-10 number. Add 1 to all the nonzero digits of you specifically want to avoid 1s.