## Randomness is Weird

When dealing with the infinite, statements about random objects probably don't mean what you think they mean.

## An Annotated History of the Reals

In the beginning, there was nothing, \( 0 = \emptyset \). Then we realized *it* was some*thing*, \( 1 = \{ \emptyset \} \). Then we wondered, why not have another thing? \(2\). And another thing, \(3\). And another, \(4\), and another, \(5\), and another, \(6\), etc. Just like that, we had the **natural numbers**!^{1} And …

## Hmm, Ordinal Numbers...

In the last post, Why Ordinal Numbers, I had intuitively guessed that I would be left with a perfect set after enough application of derived sets on \({S}\). By the end, I gave an example of a set that had a nonempty “infinite” derived set, \({S^{(\infty)},}\) that was not …