HonoraryMancunian@lemmy.world to Showerthoughts@lemmy.worldEnglish · 8 months agoA number chosen truly at random will have infinite digitsmessage-squaremessage-square31fedilinkarrow-up115arrow-down134
arrow-up1-19arrow-down1message-squareA number chosen truly at random will have infinite digitsHonoraryMancunian@lemmy.world to Showerthoughts@lemmy.worldEnglish · 8 months agomessage-square31fedilink
minus-squareCrul@lemm.eelinkfedilinkarrow-up7·edit-28 months 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-squareHonoraryMancunian@lemmy.worldOPlinkfedilinkEnglisharrow-up3·8 months agoYes real numbers, but as far as I’m aware it’ll happen for integers too almost surely
minus-squareCrul@lemm.eelinkfedilinkarrow-up4·8 months 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-squareCrul@lemm.eelinkfedilinkarrow-up2·8 months 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.