What you know about infinity? 5 things your ass needs to know.

Infinity is one hell of a misunderstood concept y’all. I’m going to take the time out of my busy-ass day to give you 5 things you need to know about it. PLEASE settle your ass down and pay attention.

1.  Infinity. Is. Not. A. Damn. Number.

It’s an idea, my babies. A concept. The word comes from the Latin (yeah, that’s right) word infinitatem–meaning “boundlessness, endlessness” (big ups to etymonline.com for that one). Can’t no fucking number equal infinity.

2.  $\dfrac{1}{0}=\infty$

Calm down, I know what I just said. To be fucking clear, when I say $\dfrac{1}{0}=\infty$, I’m not saying “one divided by zero equals infinity.” Shit no. How you gonna divide something by zero? What I mean is “one divided by x approaches infinity as x approaches zero.” Observe:

$$\dfrac{1}{1}=1$$

$$\dfrac{1}{0.5}=2$$

$$\dfrac{1}{0.01}=100$$

$$\dfrac{1}{0.00001}=100,000$$

See the trend, professor? As the denominator approaches zero, the value of the fraction increases dramatically–it will only keep getting greater and greater. It approaches infinity. Why doesn’t it ever get there? See number one, asshole.

This here is the concept of a limit–which is basic shit for calculus. I’ll spread the good news on limits another time.

3.  Don’t assume you can pull this shit or anything like it:  $\infty+\infty=2(\infty)$

Infinity isn’t a number. Can’t say that shit enough. Normal operations (addition, multiplication, etc.) as most people know them just don’t work on it, because those operations were created, in general, for real numbers. Through the study of limits and some other boojie mathematics, we can do arithmetic with infinitudes to an extent, but don’t try it without a grownup present, jabroni…

4.  $\dfrac{\infty}{\infty}=1,2,3,4,5…$

This shit is bonkers. Remember me saying arithmetic rules don’t apply the same way? We could make $\dfrac{\infty}{\infty}$ be pretty much any number we want, depending on how we define it. Again, limits let us do shit like this. Looks like I’ll have to cover them sooner than I thought.

5.  There are different kinds of infinity. Hell yeah, there are.

Think about the integers. That’s 1, 2, 25, -73, etc. No decimals or any shit like that. We say there are infinitely many integers–they go on forever. We also say that the integers are “countable.” Start with 1, next number is 2, then 3, and so on. So then, you ready for this? The integers are “countably infinite.” Original as hell.

Now, think about the real numbers. That’s all the integers plus everything in between. Anything that can be put on a number line. Can you count them shits? Start with 1. The hell is next? 2? Nope. 1.5? Wrong. 1.0001? Fuck this. There is no “next.” We call these numbers “uncountably infinite.”

The real numbers is a bigger set than the integers. BOOM, BITCH! They are both infinite sets, but since the reals are not countable and the integers are, there  are “more” reals. Explaining that shit will be a post in itself… later.

Educate yourself on this shit, expand your mind, teach others, fight ignorance.