Infinity Comes in Many Sizes

In 18 73, german mathematician georg cantor shook math to the core when he discovered that real numbers outnumber natural numbers. Cantor's continuum hypothesis asserts that there are precisely al f one real numbers. But cantor couldn't prove it and in 19 hundred mathematician david hilbert put the continuum hypothesis first on his famous list of 23 math problems to solve. In addition to the continuum hypothesis, most questions about infinite sets turn out to be independent of z f c as well. We just need new tools to figure out what size infinity is.