Phil's on Vacation #2
I know enough about the mathematics of infinite numbers to realize that the Absolute Infinite + 1 = the Absolute Infinite. You can also multiply the Absolute Infinite by any number no matter how high, and you'll still get the Absolute Infinite. It's also immune to being raised to any power. Even the Absolute Infinite to the power of the Absolute Infinite is still the Absolute Infinite.
It's really kind of a boring number. But if you think about it too much, you'll get dizzy.
Comments
Depends on your axiom system. Under the tradition axiom system, (ZFC), there is no set with this number as it's cardinality. Instead it is part of a completion of this number system (if I understand correctly). So existence isn't natural. Uniqueness is also a bit iffy. If you don't have the axiom of choice, then you can have infinite cardinal numbers which aren't comparable, ie, the trichotomy condition (that two numbers are either equal or one is greater than the other) can fail. Under such circumstances, it may be possible to build a number system where there are more than one such numbers.
Finally, there is a practical limit to the usefulness of infinite cardinal numbers. Humans can't store or even generate generic members of a set that larger than countably infinite (I assume here that you are restricted by discreteness, if in a digital situation and/or noise if you're working in an analogue or quantum analogue system).
Posted by: Karl Hallowell![[TypeKey Profile Page]](http://www.blog.speculist.com/nav-commenters.gif)
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May 22, 2006 10:57 AM