3 ms·
>One of the properties that π is conjectured to have is that it is normal conjectured Glad to see one of my pet points of pedantry come up. No non-constructed
by windward 4mo ago
>One of the properties that π is conjectured to have is that it is normal
conjectured
Glad to see one of my pet points of pedantry come up. No non-constructed irrational number has never been proven to be normal or disjunctive.
- oofbey 4mo agoThat’s a lot of negatives!
- School-Cotton 4mo agoWhat do you mean by "non-constructed" here?
- pocksuppet 4mo agoYou can design a number. Just take all finite digit strings in order of length and numerical order: 0.123456789 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 ... 99 000 001 002 ... 999 0000 0001 ... obviously it contains every finite digit string in base 10. I can't prove the digits are uniformly distributed in every base - you'd have to be more clever but you see the idea.
- School-Cotton 4mo agoBut pi is also "constructed", in the sense that you can write down a constructive definition for it, for example \sqrt{6 \times \sum_{k=1}^\infty \frac{1}{k^2}}. So I suppose maybe OP meant we haven't proven any number to be normal (or not) that is not designed to be normal (or not) ?
- pocksuppet 4mo agoThat's what it means.
- niggischiggi 4mo agoYou must be fun in RL.
- vbarrielle 4mo agoChaitin's constant does not count? Depends on your definition of constructed, but contrary to "easy" normal numbers such as Champernowne's constant, it's not defined by its sequence of digits.