killing raven sun wrote: ↑Sat Dec 29, 2018 7:09 amno its not, you cannot "remove" elements from infinity, if you can the set is not infinite, additionally you also create "unequal" infinities where i=i-1 must be true, which of course cannot happen, if you are just making stuff up without regard for logic then why not just put everyone in one room?

Sure you can remove items from an infinite set, and the result will still be infinite...

use the set of numbers.

1 2 3 4 5 6 7 8 ... to infinity....

remove the first - you have

2 3 4 5 6 7 8 9 ... to infinity

both sets have the same cardinality, which is why the set of odd numbers is the same as the set of all the odd and even numbers.

They have the same cardinality.

But the set of the Reals is a larger infinite set...

and i'm not making this up, Hilbert's Hotel is a well known mathematical phenomenon demonstrating the nature of infinity.