Donâ€™t flip the fuck out.
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.
Let x equal .999999999â€¦Then 10x would equal 9.9999999999â€¦.We therefore have the following:
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.
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.
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.
SUCK FARTZ, HATERZ.
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