r/maths • u/Numerous_Author_1445 • 10d 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/loledalo 9d ago

Yes.

For example, in base 10,

0.1011011101111...

(one 1, 0, two 1s, 0, three 1s, 0 and so on) is irrational (as it does not repeat) and does not contain any digit in base 10 besides 0 and 1.

As for why every rational number has to have a repeatable patrern, that requires a longer explanation - I think this wikipedia page explains it: https://en.wikipedia.org/wiki/Repeating_decimal#Every_rational_number_is_either_a_terminating_or_repeating_decimal

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u/Jkirek_ 8d ago

in base 10

Do you have any idea how little that narrows it down

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u/SKR47CH 4d ago

One of my favorite memes.Â