Well no, like has been pointed out, you can add to infinity, it would simply stay infinity. There are more than 1 infinities, and some are larger than others (no, I cannot explain this (sorry), at least not like it should be explained with math equations). |

Hi Huntard, popped in to visit and just noticed your post. Cantor was a bit of an interest of mine a few years back so I feel I can explain (maybe my terminology may not match Cantor Exactly).

The first infinity (Aleph-0) is the amount of integer (whole) numbers from 1, or any starting point to 'infinity' (or negative infinity). eg 1, 2, 3, 4 etc. No matter which infinite set of whole numbers you take they can be 'mapped' to any other 'infinte' set of integers by applying any consistent rule you can make up.

To map the axis 0-to-infinity to "-infinity to +infinity", you can apply a rule such as :

0=0, 1=1, 2=-1 ,3=2, 4=-2 etc, etc |

This proves that Aleph-0 * any number = Aleph-0. Adding an extra number in is done the same, so proving Aleph-0 + any number = Aleph-0 as well.

The value 'c' (continuum) is the other important infinity, suspected by Cantor's Hypothesis, but not proved to be, 'Aleph-1' the second lowest infinity. c is the number of points in a line. Many properties of this infinity are totally different from Aleph-0. You can map Aleph-0 into 'c' but not the other way around (Cantor's Theorem provable by the diagonal argument). This provides a direct proof that there are more than one infinity, and some are bigger than others.

The difference may be clearer if I point out that Aleph-0 is the size of the set of all numbers with a finite number of digits (the set of all finite strings), while all the entities in the 'c'-sized set have an infinite number of digits (after the decimal point) (the set of all infinite strings).

A consequence of how this works is that any Aleph-0 set can be ordered in a hypothetical 'list' from 1 to infinity without missing any. Trying to order a 'c' sized set into a sequential list turns out to be theoretically impossible, which is the basis of the Cantor's diagonal argument proof.

For this reason Aleph-0 sets are referred to as "countable/countably" infinite sets and 'c' sets as "uncountable"

*Edited by jasonlang, : No reason given.*

*Edited by jasonlang, : No reason given.*

*Edited by jasonlang, : No reason given.*

*Edited by jasonlang, : No reason given.*