First, let’s agree that a number can be represented in many ways. 4/2, 30-28, and .5 x 4 all are equivalent to 2. 50/150, 2/6, and .3 repeating are all equivalent to 1/3. I’m going to assume that everyone is cool with that.

Now, let’s get to some relatively simple arguments in favor of this idea.

Algebraic argument:

Let x equal .999999999…Then 10x would equal 9.9999999999….We therefore have the following:

10x=9.99999999…

-(x=.999999999…..)

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9x=9

x=1

We started with x=.99999….but ended with x=1. We violated no laws of algebra or arithmetic, so blame: .9999999…=1.

Number Theory argument:

If .9 repeating and 1 are not equal, there must be some value that is between them. That is to say, one way I know that .8 repeating is not equal to 1 is that the number .9 is between .8 repeating and 1. Try to think of a number between .9 repeating and 1. I’ll wait.

Multiplicative fucking argument:

We’d all agree that 1/3=.3 repeating, right? (If you’re unsure, do the long division. If you disagree, you’re a dickmonkey. Stop reading this blog and check into a zoo, where you can throw shit at strangers for the rest of your animal life.)

Ok. What is .3 repeating times 3? .9 repeating.

What is 1/3 times 3? 3/3. What’s another way of saying 3/3? 1.

Pow.

Sonofabitching Additive argument:

1/9 =.1 repeating

8/9 =.8 repeating

ADD THEM TOGETHER

9/9 = .9 repeating.

What’s another way to say 9/9? ONE.

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I understand that this idea may cause some discomfort. It is perhaps an instinct to believe that .99999999…”gets infinitely closer to 1.” But a numerical value doesn’t get closer to anything; it is where it is. It is true that .9 is not as close to 1 as .99, which is, in turn, not quite as close as .999, but .9 repeating has an infinite number of 9’s, no matter how many of those 9’s you write down.

Doesn’t make sense? Ask me about it.

Disagree? I double dog dare you to prove me wrong.

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