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26 points

Take a look at 0.101001000100001… This number is also non-repeating, but obviously doesn’t contain all numbers with finite digits.

The property you’re looking for is called to be a normal number. Pi is assumed to be one, but it hasn’t yet been proven.

However, in a sense this is an unremarkable property as almost all real numbers are normal. :)

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-2 points

but obviously doesn’t contain all numbers with finite digits.

I was just claiming possibility because we haven’t calculated the infinite string

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