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.(0123456789) is rational, though. I think the implication is that if pi is normal in addition to its other properties — specifically irrationality — that it ha
by jakelazaroff 3y ago
.(0123456789) is rational, though. I think the implication is that if pi is normal in addition to its other properties — specifically irrationality — that it has to contain all possible digit sequences.
Edit: oops, I forgot about n-length sequences of digits, .(0123456789) is definitely not normal, this is why I’m not a mathematician.
- oneshtein 3y agoPi may contain any sequence of digits but it's not proven that it contains all sequences of digits. IMHO, it's possible to construct a sequence of digits which will not be in Pi. It's easy to construct such sequence for first N digits of Pi of any length (for example, N zeroes).
- jakelazaroff 3y agoWe’re talking about a hypothetical scenario in which pi is normal, though.
- Dylan16807 3y agoConstructing things for N digit subsets can be misleadingly easy. It's easy to construct a sequence of digits that is larger than any N digit number. But it's obviously impossible for any such number to be the largest number.
- LodeOfCode 3y agoThis reasoning is true of every real number, yet it's been proven that almost all real numbers are absolutely normal and therefore contains every finite sequence of digits