@HonoraryMancunian to ShowerthoughtsEnglish • 1 year agoA number chosen truly at random will have infinite digitsmessage-square30arrow-up115arrow-down136
arrow-up1-21arrow-down1message-squareA number chosen truly at random will have infinite digits@HonoraryMancunian to ShowerthoughtsEnglish • 1 year agomessage-square30
minus-square@[email protected]linkfedilink7•edit-21 year agoI also think that’s correct… if we are talking about real numbers. People are probably thinking about integers. I’m not sure about OP. EDIT: I think it also works with p-adic numbers.
minus-square@HonoraryMancunianOPlinkEnglish3•1 year agoYes real numbers, but as far as I’m aware it’ll happen for integers too almost surely
minus-square@[email protected]linkfedilink4•1 year agoI think you’re confusing “arbitrarily large” with “infinitely large”. See Wikipedia Arbitrarily large vs. (…) infinitely large Furthermore, “arbitrarily large” also does not mean “infinitely large”. For example, although prime numbers can be arbitrarily large, an infinitely large prime number does not exist—since all prime numbers (as well as all other integers) are finite.
minus-square@[email protected]linkfedilink2•1 year agoFor integers I disagree (but I’m not a mathematician). The set of integers with infinite digits is the empty set, so AFAIK, it has probability 0.
I also think that’s correct… if we are talking about real numbers.
People are probably thinking about integers. I’m not sure about OP.
EDIT: I think it also works with p-adic numbers.
Yes real numbers, but as far as I’m aware it’ll happen for integers too almost surely
I think you’re confusing “arbitrarily large” with “infinitely large”. See Wikipedia Arbitrarily large vs. (…) infinitely large
For integers I disagree (but I’m not a mathematician). The set of integers with infinite digits is the empty set, so AFAIK, it has probability 0.