[mjw1007]

I was taught that dropping the axiom of choice was enough to make Banach-Tarski go away. That seems considerably short of "there is no such thing as an infinite number".

But the Twitter link at the top of this thread seems to have a rather more interesting way of doing so.

[thaumasiotes]

> I was taught that dropping the axiom of choice was enough to make Banach-Tarski go away. That seems considerably short of "there is no such thing as an infinite number".

The Banach-Tarski theorem is not the only theorem out there that bothers some people. Anything to do with infinities gets a large number of outraged rejections.