# 0.999... = 1

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Category
Philosophy
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One week
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One week
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Description
0.999... = 1: Prove that 0.999 (repeating to infinity) isn't equal to 1.
Proof 1:
x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1
Proof 2:
0.333... = 1/3
0.666... = 2/3
0.999... = 3/3 = 1
Proof 3:
All numbers that aren't equal to each other will have a number(s) that comes in between.
x < x+1 --- The number that could come in between of x and x+1 could be x+1/2.
So, give a number that comes in between 0.999... and 1.
You (as Con) will try to prove 0.999... (repeating to infinity) IS NOT EQUAL TO 1.
Round 1
Published:
0.999... = 1: Prove that 0.999 (repeating to infinity) isn't equal to 1.
Proof 1:
x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 1
Proof 2:
0.333... = 1/3
0.666... = 2/3
0.999... = 3/3 = 1
Proof 3:
All numbers that aren't equal to each other will have a number(s) that comes in between.
x < x+1 --- The number that could come in between of x and x+1 could be x+1/2.
So, give a number that comes in between 0.999... and 1.
You (as Con) will try to prove 0.999... (repeating to infinity) IS NOT EQUAL TO 1.

Published:
I am here to expose a lie. This is taught in official school math but is an absolute lie.

1/3 is not 0.3333.... with a '3' at the end. It is 0.333... that is eventually supposed to change into a value that is a 'third' but doesn't exist. So it will be 0.333...0333... over and over again.

The idea that because 0.999... is going on forever it's somehow less impossible or stupid than a number which doesn't have the identical digit throughout its infinite series, is nothing but pseudointellectual deception. 0.999... is meant to end in a 0 theoretically. 0.000... with a '1' at the end of 0's is not less possible to exist or less 'real' at all.

The difference between 0.999... and 1.000... either exists or 0.999... doesn't exist at all numerically and therefore it can't be equal to 1.
Round 2
Published:
Okay,
You still haven’t truly disproved proof 1 & 3 as they’re the best ones.
If 0.999... isn’t 1 then what is a number that goes in the middle to prove it.
And don’t even try to disprove 1 because it’s impossible.
0.999... = 1
Published:
The number in the middle is 0.999... with a '05' at the end. Similarly 0.999... itself has a '9' at the end that is meant to also theoretically be followed by infinite 0's (since all numbers have that following and the infinite 9's must end in a 9) so it's just as impossible of a value as the midpoint between it and 1.0000...

Scenario 1 is HOCUS POCUS BBBBBBBBBOOOOOOOOOOOOOOOOOOOOOOGGGGUUUUUUUUUUUUUUUUUUSSSSSSSSSSS
What you did with 'x' in the scenario is nothing more than a magic trick due to limitations of algebra and the fact that 0.999... is a fake value that doesn't even exist as you never reach the last 9. Try and reverse engineer it. Do it with x = 1 at the start and get me 0.999... at the end. You can't, meaning it's a pseudointellectual hoax.

Let's see Scenario 3...
All numbers that aren't equal to each other will have a number(s) that comes in between.
x < x+1 --- The number that could come in between of x and x+1 could be x+1/2.
So, give a number that comes in between 0.999... and 1.
oh. I handled that at the start of this Round.
Round 3
Not published yet
Not published yet
Round 4
Not published yet
Not published yet
--> @K_Michael
As to the number in between them, that is true as well.
Once you get to rational numbers (decimals), any 2 numbers have an infinite number of numbers between.
1 and 2 have 1.1, 1.2, 1.2
1.1 and 1.2 have 1.11, 1.12, 1.13
1.12 and 1.13 have 1.111, 1.112, 1.113 and so on.
If all numbers must have an infinite number of numbers between them. This leads to the conclusion that if there are no numbers between them, there is no difference between them.
--> @K_Michael
Repeating decimals are rational numbers.
Whole integers can be represented as fractions or decimals.
--> @AKmath
"All numbers that aren't equal to each other will have a number(s) that comes in between."
You made this up. No math textbook has ever listed this as a fact of math that I'm aware of, and I'm pretty good at math.
it's simple. 0.99999... is an irrational number, and 1 is a rational number. 0.99999... is a decimal and 1 is a whole integer. By definition these cannot be the same number as they belong to mutually exclusive categories. I could draw a Venn diagram in Microsoft Paint if that would help you understand the concept.
--> @SirAnonymous
"It will become infinitely small".
You say as if its value is changing in time. But it isnt. That is how we describe it as we try to determine its value. But when we examine it as a whole, rather then what it is gradually becoming, we look at what it ultimately is. And ultimately it ends up at 1.
--> @SirAnonymous
Ah, okay. That makes much more sense now. Thank you.
As someone who knows calculus, I find this question interesting. The answer I learned is that, while 0.999... is not equal to 1, there is no functional difference. 0.999... can get infinitely close to 1, but it will never equal one. However, the difference between 0.999... and 1 will also become infinitely small, so the difference is incalculable. So while they are not technically equal, they may as well be. (Unless you start dealing with quantum theory, but I'm not going there.)
--> @DynamicSquid
It's not a mystery for people who actually understand the math.
A preeminent determining factor is the degree of one's education.