>> You can't say that with precision, because it is infinity you are struggling with. What you can say is that for every number n there is a cube with n on it, and that every cube has exactly one number written on it.
This may be nailing it -- struggling with infinity.
When you say "every number n there is a cube with n on it", what does "every" mean. Does every number include infinity? Or should not not consider infinity to be a number? If the latter, this is probably where I went wrong.
> When you say "every number n there is a cube with n on it",
> what does "every" mean.
To be more precise, every finite number.
> Does every number include infinity?
No, in these sorts of discussions infinity is never considered to be a number. You need explicitly to be discussing transfinite arithmetic, and we're not.
> Or should not not consider infinity to be a number?
> If the latter, this is probably where I went wrong.
Absolutely you should not be thinking of infinity as a number.
This may be nailing it -- struggling with infinity.
When you say "every number n there is a cube with n on it", what does "every" mean. Does every number include infinity? Or should not not consider infinity to be a number? If the latter, this is probably where I went wrong.