You know that comment about still wanting someone to produce the logical negation of that equation...
From the definition of a Limit,
The negation of the definition of a limit:
is logically equivalent to
From the definition of a Limit,
∀ε>0 ∃δ>0 ∋ 0<|x-a|<δ⇒|ƒ(x)-L|<ε
The negation of the definition of a limit:
¬(∀ε>0 ∃δ>0 (0<|x-a|<δ⇒|ƒ(x)-L|<ε))
is logically equivalent to
∃ε>0 ∀ δ>0 (0<|x-a|<δ ∧ ¬|ƒ(x)-L|<ε)
WTF?
Date: 2009-04-16 02:34 am (UTC)"Train A leaves the east coast station at 8:00 a.m. traveling west at 55 mph. Train B leaves the west coast station at 10 a.m. traveling east at 75 mph. At what time will the two trains meet?"
I HATED those questions...
Here's my answer I actually gave on a test:
Frankly I do not care unless one of the two situations come into play:
1. I'm on one of the two trains
and/or
2. The trains are traveling on the same piece of track.
I got a point for creativity.
Re: WTF?
Date: 2009-04-16 02:36 am (UTC)Re: WTF?
Date: 2009-04-16 02:39 am (UTC)I have no time for logic.
Re: WTF?
Date: 2009-04-16 02:49 am (UTC)Besides, no one could do the problem as you specified. You neglected 1) the overall distance of track involved (we'll ignore elevation and curve radius concerns), and 2) whether either of the times were local or both referenced the same time zone.
Touchy-feelie doesn't build much stuff.
Re: WTF?
Date: 2009-04-16 03:02 am (UTC)Uh...no.
no subject
Date: 2009-04-16 03:04 am (UTC)no subject
Date: 2009-04-16 03:04 am (UTC)no subject
Date: 2009-04-16 03:07 am (UTC)no subject
Date: 2009-04-16 03:09 am (UTC)no subject
Date: 2009-04-16 03:38 am (UTC)no subject
Date: 2009-04-16 04:10 am (UTC)So what are the odds that I would click on the comments of one of the many many posts in my friend's list today and see that exact same sentence? That seems beyond serendipitous. Or have you had pizza recently?
Re: WTF?
Date: 2009-04-16 11:38 am (UTC)By education, I’m a mathematician who’s a thesis away from a doctorate. (It’s a computer science degree, but grad school for CS is essentially an applied math degree.) At least once a month or so I hear someone say, “I’m so glad someone understands it — I could never understand math!”, followed by a laugh — as if they expect me to join in the humor.
But there is no humor, and I have become tired of pretending there is.
Feelings and touchy stuff are all important, yes, but they don’t make us human. By definition, an emotion is a behavioral impulse that does not follow reason. Since animals cannot reason, that means emotion is all animals have to guide their behavior. You call it “instinct,” but let’s call it what it is: emotion.
Emotion is great. Don’t get me wrong. Emotions are important and emotions can be a lot of fun and life without emotions is rather austere. But emotions aren’t what make us human.
Reason is what makes us human. Reason is the thing that, as far as we know, only human beings can do. In all the natural world we have never seen any evidence of logical manipulation of rules by any other animal. (Parrots have some understanding of relative quantity, as do some other animals; but that’s a far cry from logic.)
When you say, “I have no time for logic,” what I hear is “I have no time to be human.” If you want to be a primate — which all of us are, make no doubt — then that’s your lookout.
Me, I’m a primate who wants to be something more, something better. And that’s why I always make time for logic.
Re: WTF?
Date: 2009-04-16 11:42 am (UTC)Well, to be fair, you could turn it into a linear equation of two variables. The time to collision is dependent upon the distance separating the trains and the relative offset of their clocks. Once reduced that far I’d call the problem complete, in that you would have completely defined the entire solution space. Once given the distance and offset, you’d have your hyperplane through the solution space.
Re: WTF?
Date: 2009-04-16 12:24 pm (UTC)However, my point was (and is) that while some have a propensity for mathematics, I do not. It makes my head hurt...exceedingly. I do simple math everyday, things that make sense to the average joe to try to explain why people have overdrafts and why their account is the balance it is.
I deal in a realm of reason and logic while my customers do not. When I said what I said, it was after a long, hard day of trying to reason with unreasonable people.
...thanks to both of you but to be honest, at some point in my day, I'm done with it all.
no subject
Date: 2009-04-16 07:06 pm (UTC)I know I didn't come up with that phrase but I've been using it on the kids for years. Chances are, whoever originally said it was also heard by the auteur of the pizza-box wit...
But it is kind of freaky to have it occur twice in one day in totally unrelated incidents. It's a message. Find the patent number for that pizza box and play it in the lottery!
no subject
Date: 2009-04-16 09:39 pm (UTC)As a friend of mine remarked, “The Big Bang Theory is not for us. It’s for people who know us and are secretly intimidated.”
no subject
Date: 2009-04-16 09:59 pm (UTC)Often not so secretly.
Re: WTF?
Date: 2009-04-16 10:17 pm (UTC)Respect engenders respect.
Re: WTF?
Date: 2009-04-16 11:28 pm (UTC)Edited, twice, to correct subtle errors.
If it helps any, I strongly doubt that you have no propensity for math.
There are certain mental disorders like discalculia (mathematical dyslexia) that devastate people’s abilities to juggle written symbols. The rest of us get our faculties crippled the more brutal way: by what passes for mathematics education.
Here’s a thought experiment for you. You’re a cop enforcing the liquor laws. You see four people. One is drinking a Coke, one is drinking a beer, one looks to be about 15, and one looks to be about 90. Which of the four do you need to check out more closely?
Most people can solve this one without batting an eyelash. You need to check the 15 year old, to make sure he’s not drinking beer. You need to check the guy drinking beer, to make sure he’s 21. But the guy who’s 90, who cares what he’s drinking? He’s legal. And the guy who’s drinking Coke, who cares how old he is? He’s legal.
You might think this problem is admirably simple. It is. Now let me phrase it like a mathematician would:
As
furrbear will affirm, this is the exact same problem, just expressed in mathematicalese.
I used to give this to new grad students in the math and computer science programs. About one in five was able to see past the rigamarole and see just how simple the problem was, and see the obvious solution.
Unfortunately, most math education in this country seems to be focused on the impenetrable words, and less on the beautiful and elegant principles beneath the words.
Neither
furrbear nor I think you’re math–dumb. Far from it. At worst, you’re a perfectly normal human being who has been mangled by a pathologically faulty educational system.
no subject
Date: 2009-04-17 01:09 am (UTC)no subject
Date: 2009-04-17 01:42 am (UTC)Thanks, Jeff.