The math level in this post may be a bit higher than the usual level in my math entries so feel free to skip it. I just have to share this because I found it absolutely amazing.
ℵ0 is a large cardinal. We just declare it to exist with an axiom that we all agree on. For all the common definitions of large cardinals ℵ0 satisfies the requirements. To a lot of people who have studied model theory and set theory this will likely seem trivial, but this was pretty mind-blowing to me.
This information is courtesy of Harry Altman.