4 ms·
Are 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
by cthalupa 7y ago
Are 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!