What is the smallest positive integer that can be expressed as the sum of eleven consecutive positive integers, the sum of twelve consecutive positive integers, and the sum of thirteen consecutive positive integers?
@Twink I can ask what ever I want. I am trying to get to grips with a topic that I am not too familiar with and maybe, just maybe, I can learn something like a new technique.
@Twink The problem then is that you'll get 3 quadratic equations that each depend on a different starting number, say $n_1, n_2, n_3$. I'm not sure you can progress from that
Have you ever seen what it is like to a be a woman online? Even if people are not aggressively obnoxious to them, they are often passively obnoxious. And entering a math den would be disaster.
@Twink It is entirely possible there ARE girls on MSE who just choose not to express their gender. But I also agree with Thomas. You can't admit to being a woman on the internet without a stream of lewd and rude comments flying your way. I don't think you'd have problems from MSE though.
@AlecTeal I have personally investigated a number of the streams of female games on Twitch.tv and found that almost universally they are subject to attacks that revolve primarily around their gender. Low-quality male streamers are ignored. Low-quality female streamers are ridiculed. Of course you don't have to take my work for it. Go to Twitch.tv and look at the chat of any female streamer
@AlecTeal It is precisely that attitude - everybody is a dick - that caused me to stop online gaming, except for contract bridge, where the players are statistically more mature.
@KevinDriscoll and @ThomasAndrews yes Halo - Xbox Live is bad - it's all like "Haha suck my dick gay boy" - yes, that'd make me the gay one.... no offense @Twink maybe.
I haven't played much in a long time, but I have a bridge web site: bridge.thomasoandrews.com with a lot of stuff that might be interesting to mathematically inclined bridge players :)
If it was just Halo, I wouldn't mind, because I don't play that game, but virtually every online game I've ever played other than bridge was filled with racist words, homophobic words, etc. Most of that is just teen boy stupidity, South Park had a funny joke about that many years ago. Cartman had learned a friend had a crush. Cartman: You like a girl? You're such a fag! That's the level of it, most of the time.
It's usually the more offensive words starting with f that are used to imply the other player's homosexuality. "Gay" is more often used for "lame" nowadays.
We had a crazy day at the office today as well......a girl moved into the office across the hall. I don't think we've had a female on the 5th floor since 19-ought8
Yeah, I get that. A long time ago, I once shared a small enclosed office with an attractive woman. I realized any discomfort was my own, but I did ask her not to wear such strong perfume. :)
@TedShifrin I don't think that would help. To be honest I've been thinking about gender issues a lot lately both in general and how it relates to my personal life. I'm not at all sure what to think.
Ah, understood (partly) @Kevin. One of my students from years ago (who transferred from Tech,actually) is now transitioning M to F. All sorts of issues some of us deal with.
@TedShifrin Yes, that is one sticky wicket. I was reading a blog for trans people a few days ago and was particularly distressed to see that one commenter insulting people who cross-dress and "just liking to play on the weekends." Makes me wonder if we'll ever grow out of our in-group/out-group mentality
Also, I realize my above comment could be interpreted that I'm unsure what my gender is and that's not the case. I'm quite clearly a cismale. I just meant thinking about how I treat others as it relates to their gender
(He was a deeply introverted man - so introverted, than when people talked about Aspergers, I always thought about him. When I met her, she was so outgoing and friendly and talkative, and I realized that he had been introverted out of fear of exposing herself. It was cover. She waited until her parents died to come out, afraid of parental rejection.)
@ThomasAndrews Illustrates a perfect point about how quickly these things move socially. A few years ago it was all the trans community could do to get people to say "transgender" or "transgendered" instead of "shemale" or some such. But now "transgendered" and "transgender" themselves are falling somewhat out of favor. My feeling is "trans" is the preferred adjective these days.
So it's all a mess of changing conventions. I find myself understanding at least 1 reason why it is comforting to have strictly-defined gender roles. The norms are always obvious.
That I totally understand. Personally, I've never known anyone pre- or mid- transition. Or perhaps I have and didn't notice; in which case good for both of us.
Yeah, one advantage if nerd-dom is that, sometimes, we just miss stuff that would cause others to be awkward. Or we are just always awkward, and no more or less awkward with "different" people. :)
@KevinDriscoll Aside for the abusive parts, the fact that he's deliberately steering the conversation into the realm of the (far) off-topic, is enough for a short suspension
@AnthonyCarapetis my definition of submersion is that is differential at every point is surjective, the statement im trying to prove is this: Let $f: M \to B$ submersion: A map $g: B\to N$ is smooth if and only if $g\circ f$ is smooth
@ADR: you need to know that at least locally, you can find a submanifold $\Sigma$ of $M$ such that $f$ restricted to $\Sigma$ is a local diffeomorphism. Restricting $g \circ f$ to $\Sigma$ will give you what you want I think.
@ADR: locally. So the image of a small enough open set in $\Sigma$ will be an open set in $B$. Since smoothness is a local property that's all you need anyway.
