Archive - Feb 21, 2008

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A mathematical look into the limit joke

Edit: Melis have removed this joke from MIT admission blog after my comment on the 10 things I love about MIT

OK, Mgccl, I have removed the joke from the math entry. I had received your previous email and didn't remove the joke at the time because I thought that it was clear that these were jokes and therefore not factually accurate (I hope you don't take everything in xkcd as true. Helicopters don't get cancer.) While it is admirable that you took the time to correct the joke, for everyone's future reference, it's advisable NOT to use jokes as your source of knowledge on tests...textbooks are more reliable.

Some time ago, I had pointed out a mathematical flaw in the famous study = fail joke.
Now, I saw another unforgivable math joke that's completely wrong.

It's featured on MIT Admissions blog. No one commenter spotted it? Come on MIT, you could do better.

Someone is WRONG on the internet. and I have to fix it. I love how xkcd comic knows exactly what I'm thinking about.
What do you want me to do?  LEAVE?  Then they'll keep being wrong!

Let's not talk about the implied stereotype of women in mathematics that tries to make this joke funnier, because that's nothing compare to getting the basic understanding of limit wrong.
Definition of limit according to wikipedia:

Let f be a function defined on an open interval containing c (except possibly at c) and let L be a real number.

\lim_{x \to c}f(x) = L

means that

for each real ε > 0 there exists a real δ > 0 such that for all x with 0 < |x − c| < δ, we have |f(x) − L| < ε.

A very convinient graph of the function 1/(x-8)

What did you know? according to the graph, there is no limit.
There are, of course, left-hand and right-hand limits. So the real joke should be something like this.
\lim_{x \to 8^+}(\frac{1}{x-8}) = \infty
\lim_{x \to 8^-}(\frac{1}{x-8}) = -\infty

Really, letting math jokes like this going around can hurt people on their tests, I learned it the hard way.

There is a interesting point I can make to make this math joke correct.
If we don't consider this problem in the usual first year college calculus's extended real number line, where there are 2 different kind of infinity. \infty and -\infty, but to consider it in real projective line, then that is correct.
But really. How can a student can't understand the material of 1st year college calculus and working on calculus on real projective line?

Honey Pot that kill bots