mdalmostdn

Background
One of the most fascinating and fun concepts in all of mathematics is the notion that infinity is not "one size fits all." The concept of different-sized infinities has captured the imaginations of mathematicians, scientists, and philosophers alike.

Question
Research the topic of sizes of infinity and post your answer to one or more of the following questions:

• Other than the two sizes of infinity, countable and uncountable, are there more? If so, how many different sizes of infinity are there?

• Since countable means having a one-to-one correspondence with the Natural numbers, and Cantor's second diagonal argument seems to imply that uncountable means having at least one element more than that, just how much bigger is uncountable than countable?

• Is there another size of infinity in between countable and uncountable? Or discuss other interesting aspects of this topic that you find during your research.