## 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 something, $$1 = \{ \emptyset \}$$. 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 …