Nov 15, 2025
I was a bit overwhelmed earlier and decided that the only solution was to go on a tedious pedantry rampage in latex. It did work. I am feeling better.
Here is a very simple proof of a very simple thing. (that isometries must be injective). You can weaken it on the left to finish adding how metric spaces and the reals work, but I ran out of space, and it was fairly trivial to do, and I was already feeling better.
There's not really a point to doing things this way most of the time and it isn't hard, just somewhat tedious. And this is longer than it really has to be. But, for anyone who hasn't seen what a formal math equivalent of someone saying a lot of words and not getting a lot of meaning across, this is it.
