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cka

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Yeah, and constructability is usually handled by proving that a length is constructable if it lives in an iterated quadratic extension of the rationals. Pi does not lie in such an extension, so is not a constructable length (and neither is its square root).

Or 'caw' if you want to change the whole word, even if cursor is in the middle somewhere. I read it as "change a word".

I'm a math PhD, was a tenured professor and then transitioned to industry. We've got two humanities PhDs that work as QA testers on our team. They're both fantastic, especially in thinking about either big picture questions or nuanced takes that others missed out on.

There's a common workflow I use at work that involves taking the default 10 times before inputting what I need to use. I do double shave and a haircut quickly instead of counting return presses.

A similar annoyance is the fact that excel's undo applies to all open excel files. Make a change in a.xls, make a change in b.xls. if you ctrl-z twice with b.xls focused, it'll undo both of the above changes!

This has bitten me more than once. Does anyone actually want this behavior?

I can't speak for the op, but in Minnesota (in the northern part of the US), there are days in the winter when the temperature gets as low as -30F (~ -35C) with very high winds. This can make for very dangerous travel. Occasionally there are snow storms that make the roads impassable for part of the day.

On these sorts of days, the schools are sometimes closed to keep people off the roads.

Homology 7 years ago

A curve is a 1-dimensional space. Even though you draw a picture of it in a 2 (or maybe higher?) dimensional space, you should think of the set of points in the curve as being the only points that we care about.

In a closed curve, you can never fall out of the space by moving around in it. In a curve with endpoints, you can fall out of the space by walking across one of the endpoints, so the endpoints are considered to be boundary components.

Bad. I've suffered from depression for ages. I'm an academic teaching at a small college in a small rural town. I wish I could regularly see a therapist, but there's no one within an hour of where I live. Definitely feel trapped.

Further evidence that e^{ix} = cos(x) + i sin(x) is natural is that it fits in nicely with power series representations. If you define cos(x), sin(x), and e^x by their power series centered at 0 then it's straightforward to see that substituting ix into the power series for e^x yields the sum of the power series for cos(x) and i*sin(x) (as long as you accept that theorems about absolute convergence and rearranging terms extend to the complex numbers).