4 ms·
>What if you have 0.9̅4? Well, you fundamentally can't. If the 9s go on for forever then you never reach a point where you can add the 4. The definition of inf
by cthalupa 7y ago
>What if you have 0.9̅4?
Well, you fundamentally can't. If the 9s go on for forever then you never reach a point where you can add the 4. The definition of infinity precludes anything after infinity, because it never ends so you can never get there.
- jefftk 7y agoIn this alternate number system you can think of it as a tuple: (.9̅, 4). Which is larger than (.9̅, 3) and smaller than (.9̅, 5).
- ubercow13 7y agoThat is, until Cantor showed otherwise
- cthalupa 7y agoAre you saying that Cantor showed you can have 0.9..4? I'm not even remotely an expert here, so I might certainly be wrong, but I don't understand how Cantor's theorems show an ability to stick a finite number and stop on the end of an infinite number.
- ubercow13 7y agoYes, one thing Cantor showed is that it is somehow meaningful to define numbers like infinity+1, where there are an ordered infinity of elements followed by one more element. Sets like this are called ordinals https://en.wikipedia.org/wiki/Ordinal_number https://en.wikipedia.org/wiki/Ordinal_number So you could, if you like, define 0.9...4 to be a bunch of digits indexed by the ordinal ω+1. However the thing you have now defined isn't really a representation of a real number any more, unless you just ignore all the bits after the ... I guess.
- cthalupa 7y agoHuh, interesting. Looks like I've got some more reading to do. Thank you!