-5=5

[Doom]

Huh, that's cute. Don't think I've seen that before.

You're off by a factor of two, but I'll concede that's a quibble under the circumstances.

Now do you want to tell me how you read

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a Σ b^n

where the sum is as n varies from 1 to 5?

As per wikipedia (I don't feel like digging out a book and shooting another video), and assuming that "a" and "b" are simply numbers, that notation means the same thing as (sigma) ab^n, it just saves time and calculation effort to factor out the "a" and put it in front. Note how I appeal to a definition, instead of merely winging it.

To be perfectly clear, you could write "a (sigma b^n)"....but the whole point of defining things to a cleaner notation is to save time, even a pair of parenthesis.

Now, for the idiotic "-1^2" thing you keep harping on

It really seems like you've changed your tune quite a bit on this topic.

We've already established that informally, it can mean whatever someone wants it to mean ("lose a penis and gain 2 breasts", for example)...the point is to establish what means formally, according to the actual rules, so that folks that actually care about details have some means of making the calculation the same way and understand they're speaking the same language to each other. Just because it's possible someone ignorant might say something detracts nothing from that goal.

Or maybe it is all a grand conspiracy. Whatever.

But you're missing the larger point, which is that people who use math in real life don't worry about that.

You know, it's odd to see you sneer so much at any applied math, and talk about your very abstract specialization....and come back and say to ignore details because folks in "real life" don't worry about it. You gave 3 links to wiki a few posts back...you want to tell me which of those subjects applies to people in real life?

math department has to teach the calc classes because the applied mathematicians have money and we don't.

And another little sneer to the real life folks that do worry of such things. Those guys that pay attention to details like it matters rather bug you, I suspect.

I actually understand what's going on under the hood.

Oh yes, you've shown your 'under the hood' stuff, like confusion with order of operations, worrying about R being negative in the graph of a circle (and not even knowing a circle when you see it), not knowing about the "1/2" that goes in front of the formula you used above and other little things. Piffling stuff individually, I admit, but that's alot of minor screwups for a guy claiming a particularly deep understanding of the concepts.

I'm reminded of a hiring comittee I was on a few years back. A candidate gave his 10 minute talk, and had as many errors as you did in that brief period; we didn't hire him because we all agreed he was incompetent, if a nice guy. That said, you have at least convinced me you're a mathematician, just by pretty much doing a problem you didn't have to do (but why do you write in the plural in your solution but singular in your posts, kind of makes me think there was more than one person answering the question).

For what it's worth, a measure theorist, not an abstract algebraist, would be in a better position to claim real under the hood understanding of integration.

[Grek]

If I put -1^2 into google, Wolfram|Alpha or Mathmatica, I get -1 as the result. (-1)^2 returns 1 as the result, and -(1^2) gets me -1. This seems to support the notion that for all practical purposes, you're better off assuming that -1^2 means -(1^2) rather than (-1)^2 whenever you can't get clarification. Was that so hard?