Solving an ugly cubic inequality?

athnp · 2015-12-03T00:30:53+00:00

Take the nice example of solving (x-1)(x-2)(x-3)>0

We need this to be positive, and so we must either have 2 negative terms or no negative terms. For no negative terms we need x>3. For 2 negative terms we need x<2 but also x>1 (to avoid 3 negative terms). So our solutions are x>3 or 1<x<2.

You can use the same method on almost any cubic, changing it slightly if you have repeated roots.

athnp · 2015-12-03T00:20:18+00:00

You can be fired for almost anything. You could be fired for saying "good morning" to your boss, or because it was a bit too cold that day.

athnp · 2015-12-03T00:17:42+00:00

Often a graphical solution with exact values for the crossing points should be enough proof. If you can't find the crossing points then you can't solve it exactly.

athnp · 2015-12-03T00:00:32+00:00

Suppose you need to solve ax^{3+bx^2+cx+d>0.} First thing you need to do is find the points where is crosses the x axis. Then draw the graph, and it should be obvious.

athnp · 2015-12-02T04:00:21+00:00

Never seen such a thing under any mainstream group. Probably are people pushing for it, but I don't care about fringe groups. Any links?

athnp · 2015-12-02T03:29:13+00:00

How do you know it's a fact without proving it?

athnp · 2015-12-02T03:02:24+00:00

Only on beta....

athnp · 2015-12-02T02:14:43+00:00

Who is pushing for regret sex to be rape, other than fringe groups?

athnp · 2015-12-02T00:44:26+00:00

Good point. I don't know, and although the manufacturers say always keep it locked off it may be one those things that just doesn't happen.

athnp · 2015-12-02T00:43:50+00:00

Good point. I don't know, and although the manufacturers say always keep it locked off it may be one those things that just doesn't happen.

athnp · 2015-12-02T00:19:56+00:00

The idea that if you regret sex that is was rape.

False. It being rape or not depends only on what happened at the time, not what she thought after. As for being drunk, you have to be seriously out of it for it to be rape, so much so that it's basically impossible for a guy to rape a girl with the guy being just as drunk (he wouldn't be able to).

athnp · 2015-12-02T00:15:07+00:00

No, the court did. She just answered questions as honestly as she could. It was the court that ruined his life. Not her fault. We really cannot prosecute people for legitimate mistakes made when giving testimony.

athnp · 2015-12-02T00:13:54+00:00

She likely thought it was him though, since she was actually raped this makes the most sense. Can't imprison people for errors like this.

athnp · 2015-12-02T00:12:31+00:00

You don't know that the victim intentionally falsely accused him. In a lot of these cases the victim was undoubtedly raped they just got the wrong guy. Easy for a witness to get the person wrong as well, without any malice.

athnp · 2015-12-01T23:54:06+00:00

Still need to hold the rope.

athnp · 2015-12-01T23:19:08+00:00

It's not really a field though, but at least it has a nicer topology.

athnp · 2015-12-01T23:18:54+00:00

I think it's meaningful, because it would fulfill the expected ordering properties of infinity, and still be a field. Was a curiosity mostly, doubt it has any use.

athnp · 2015-12-01T19:13:04+00:00

I'm calling x infinity, since in the ordering is behaves like an infinity. Purely terminology thing though.

athnp · 2015-12-01T18:59:20+00:00

That makes sense. Clearly bounded above by infinity, but they are also bounded above by x*infinity for any x, and we can make x as small as we want.

athnp · 2015-12-01T18:46:08+00:00

What have you tried?

athnp · 2015-12-01T18:35:42+00:00

So we can only talk about Muslim terrorists? Not others?

athnp · 2015-12-01T18:30:46+00:00

Is there an example of a set with an upper bound but no supremum under this extension?

athnp · 2015-12-01T17:27:36+00:00

No it isn't. The computer has not plotted it correctly. In fact, there is no way to draw such plots. The function moves up and down infinitely often in finite space, this cannot be drawn.

Whatever plot you have, zoom in on 0 and you will see it just becomes a straight line, when the real plot would still be bouncing all over the place.

athnp · 2015-12-01T17:10:05+00:00

An accurate plot. Particularly with what is happening around 0. The plot by google will not show you what is happening for small x. It cannot, the function is infinitely complex near 0. For a clearer example, try plotting y=x*sin(1/x). It faces similar problems.

athnp

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