kogasa

That's not a metric. In any metric, distances are positive between distinct points and 0 between equal points

That's not relevant to what they said, which is that distances can't be imaginary. They're correct. A metric takes nonnegative real values by definition

foo terminal

foot

CSS is still used. Modern web toolkits like bootstrap and tailwind can reduce or eliminate the need to write CSS explicitly. Some tools like Sass extend CSS. They all generally produce regular CSS that gets read by the browser.

It's not all of Microsoft, you just can't download ISOs from their website.

R^(3) specifically

Did they teach you how to formulate thought experiments in the shop?

Yeah, basic graduate level math is a lot more useful than whatever you do with your life to warrant such an attitude.

Specifically, the thing that exists is a regular homotopy of immersions from the standard embedding to its opposite. The "rules" aren't supposed to be self evident, they're part of a broader context in topology

The eigenvalues of a diagonal matrix are the values on the diagonal. Diagonalizable matrices' eigenvalues can be determined by diagonalizing them and looking at the entries on the diagonal.

It's interesting because it's highly counter-intuitive that such a thing is possible. It's not supposed to be useful except as an example of a false intuition, which can remind us to be careful in our reasoning.

Microsoft blocks people from downloading stuff all the time for unknowable reasons. You have to either reset your IP or go through customer support to fix it. I did the latter and they did not tell me why I was blocked in the first place.