That's really cool. However it's important to note that it nonstandard analysis does not 'live' in the real numbers. It turns out the hyperreals aren't even a m

That's really cool. However it's important to note that it nonstandard analysis does not 'live' in the real numbers. It turns out the hyperreals aren't even a metric space! I'm not intimately familiar with them though, and have heard that they are a lot more lucid abstraction for some things when compared to calculus on the reals.