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This is not necessarily true. Pi might not repeat but it could at some point - for example - not contain the digit 3 anymore (or something like that). It would
by _fizz_buzz_ 2y ago
This is not necessarily true. Pi might not repeat but it could at some point - for example - not contain the digit 3 anymore (or something like that). It would never repeat, but still not have all conceivable information.
- pilaf 2y agoBut the number 3 is there just because we decide to calculate digits in base 10. We could encode Pi in binary instead, and since it doesn't repeat it necessarily will never be a point where there will never be another 1 or a 0, right?
- bubblyworld 2y agoThat's true - you can quite easily prove that an eventually constant sequence of decimals codes for a rational number. But it's also true that pi may not contain every _possible_ sequence of decimals, no matter what base you pick. Like the Riemann hypothesis, it seems very likely and people have checked a lot of statistics, but nobody has proven it beyond a (mathematical) shadow of doubt.
- _fizz_buzz_ 2y agoObviously, it was just an example to illustrate what a non-periodic number could look like that doesn’t contain all possible permutations. If the number never contains the digit 3 in base 10 it will also not contain all possible permutations in all other bases.
- deleted 2y ago[deleted]