## A Conversation for Bigger and Bigger Infinities

### Set theory

dim12trav Started conversation Jul 25, 2003

What the author has failed to mention is there are sets that cannot be numebered. (Indenumerable) such as the real numbers. What that means is simply there is no next number.If you start with 0 what is the first number... well an infinite grouping of zeroes followed by a 1 would be the first but how many zeroes is that?

This indenumerably infinite set has been designated aleph 0 (given some Hebrew letter designation and set aside). There are other even larger sets. Such as the indenumerable set of indenumerable sets (designated C) which is not the speed of light, ala Einstein.

Yes there is much fun associated with infinity

### Set theory

MuseSusan Posted Mar 24, 2004

Yes, it's fairly simple to prove that the set of real numbers is indenumberable (or "uncountable" as I learned it), once you define a countable set. But it might be better to create a whole new entry on countable and uncountable sets, instead, because there's so much that can be said about them.

### Set theory

MuseSusan Posted Mar 24, 2004

Okay, I lied; there's already a bunch of entries dealing with countable and uncountable sets.

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