# Limits, Infinity, and the Female Student

I’ve observed this a few times in the realms of social sharing services, and it never fails to infuriate me in the sort of mild, simmering, toothache fury that developes if one spends long looking at socially shared images. Let’s start with how it’s obviously fake. As in, the situation described did not occur and someone is making it up to be funny. And, I’ll admit, it *might* be funny if it were in any way plausible – but it’s not, and the depths of its implausibility are so that here I am writing about it. The only way out is through.

First of all, the crux of this joke is how the student doesn’t realize the infinity sign (\(\infty\)) and a sideways eight (8) are different. Maybe things are different now, but when I was in school, introductory calculus was something for high school seniors or college freshmen, *i.e.* seventeen and eighteen year olds. Here is what this joke is asking us to accept: that an American who has spent almost two decades alive has somehow managed to avoid the infinity symbol, which has permeated pop culture and jewelery to such a degree it’s close to becoming meaningless. A third grader, maybe. But an American college student? Forget it.

Suppose the student isn’t American? I can’t really comment on the ubiquity of infinity symbol worldwide, but the only bit of knowledge we have about the student is her gender. Yes, whoever invented this situation thought it would be funnier and/or more plausible if the person who was hilariously bad at math was female. Ha ha ha, math is hard, let’s go shopping, right?

If that’s not enough, let’s look at the math itself. The horrible, stupid irony is that this image, which is supposed to be making fun of women who can’t do math, can’t do math itself. The expression that our imaginary professor spent various lessons and examples explaining, $$\lim_{x \to 8} \frac{1}{x-8}$$ is not defined. This is actually pretty easy to see, as when \(x = 7\) the function is \(-1\), and when \(x = 9\) the function is 1. So when \(x\) approaches 8 from above it tends towards positive infinity, and when it approaches 8 from below it tends toward negative infinity. Thus, the most you can really say is $$\lim_{x \to 8^{+}} \frac{1}{x-8} = \infty$$

Thus: joke author writing implausible, unfunny joke in which imaginary woman flubs a math problem actually reveals self to be even worse at math than his target.