First, letâ€™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. Iâ€™m going to assume that everyone is cool with that.

Now, letâ€™s get to some relatively simple arguments in favor of this idea.

Algebraic argument:

Let x equal .999999999â€¦Then 10x would equal 9.9999999999â€¦.We therefore have the following:

10x=9.99999999â€¦

-(x=.999999999â€¦..)

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9x=9

x=1

We started with x=.99999â€¦.but ended with x=1. We violated no laws of algebra or arithmetic, so blame: .9999999â€¦=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. Iâ€™ll wait.

Multiplicative fucking argument:

Weâ€™d all agree that 1/3=.3 repeating, right? (If youâ€™re unsure, do the long division. If you disagree, youâ€™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. Whatâ€™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.

Whatâ€™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 .99999999â€¦â€gets infinitely closer to 1.â€ But a numerical value doesnâ€™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 9â€™s, no matter how many of those 9â€™s you write down.

Doesnâ€™t make sense? Ask me about it.

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