Quote:
Originally Posted by GHI  Actually... no.
First of all, w is not a "cardinal" but an ordinal number.
Secondly, w+1 is not equal w. Their cardinality is the same (both have a cardinality of Aleph_Null) but the numbers are not the same.
What is true, is the 1+w=w. Addition of ordinals is not commutative, you see...
Ah, the joy of mathematics. The joy of Absolute Truth. 
And now, we return to our regular bickering... er, regular program. Back to you, guys. |
actually...yes , "w" or "Omega" is a cardinal. w cannot be mapped one-to -one into any of the finite numbers before it.
Besides that all of the alephs are often referred to as "large cardinals, infinite cardinals or transfinite cardinals"