# Proving Cardinality

• Nov 30th 2008, 11:14 AM
Ellis
Proving Cardinality
Hello,
Urgently need some help with some Mathematical Communication.
The question is:
Show that the set of all odd square numbers {1,9,25,49,...} has cardinality ℵ0 [aleph-zero].

Any ideas? (Worried)
• Nov 30th 2008, 11:31 AM
flyingsquirrel
Quote:

Originally Posted by Ellis
Show that the set of all odd square numbers {1,9,25,49,...} has cardinality ℵ0 [aleph-zero].

The \$\displaystyle k\$-th non-negative odd number is \$\displaystyle 2k-1\$...

Can you use this to find a bijection which maps \$\displaystyle \mathbb{N}\$ onto \$\displaystyle \{1,9,25,49\ldots\}\$ ?
• Nov 30th 2008, 12:16 PM
Ellis
Cardinality of R
What is the largest cardinality, because surely I can start with the cardinality of the set of all Real numbers and then work from there?
• Nov 30th 2008, 12:32 PM
flyingsquirrel
Quote:

Originally Posted by Ellis
What is the largest cardinality

I don't know.
Quote:

because surely I can start with the cardinality of the set of all Real numbers and then work from there?
I don't think so.