.999... is exactly equal to 1

I'm pretty bored so I was wondering to post a debate to see if anyone disagrees with this. Just to confirm the resolution is as follows:

.999... = 1

Definitions
.999... refers to .9 with recurring nines
1 refers to the real number, 1
= means is exactly equal to

.999... is exactly equal to one

I'll let my opponent start.

hello, to everybody brave enough to read this argument, and thankyou to my opponent for this very entertaining topic. I about started laughing because of how interesting, and simply different of a topic this is, compared to most.

I stand in negation to the topic, that .999, reccurring is exactly equal to 1

In it's own, the topic itself contradicts itself, and proves my side correct.

this is a topic, that just requires common sense, and I'm positive that all of the voters have it.

no matter how long you type it in, .9999999999999999999999999999999999999999999999999999999999999999999999999999..........

no matter how many nines you add to it, it will infinitely be less than 1.

you may round the number up to one.....

But this topic says it is exactly one.

I just proved this wrong, .999...... will NEVER be EXACTLY 1.

Vote with me in Negation.

Thankyou

I'd like to thank my opponent for taking this debate, although admittedly this is not really a topic that is open to debate. There are many mathatical proofs for this, and I will go through one for you so hopefully my opponent and the voting audience can see why they should vote PRO.

Let x = .999...
10x = 9.999... (multiplying RHS and LHS by 10)
10x - x = 9.999... - x (subtracting x from both sides)
9x = 9
x = 1
.999... = 1

This is a very simple mathematical proof for my position, which I am sure my opponent will find hard to poke holes through. Nevertheless, I wish him the best of luck.

There are always and will always be errors in math. We live in an imperfect world. The resolution states that .999 is exactly equal to 1. Using mathmatics, multiplication and suptraction, make it so that it is no longer .999... Using mathematics goes against his resolution, so regardless what mathematics can do to it, .999 is not exactly equal to 1. It will come close to 1, but it never will be 1

My opponent has offered little to counter my resolution that '0.999... is exactly equal to 1'. As it stands now, the burdens stand as follows:

The task of PRO (myself) is to demonstrate that 0.999... is exactly equal to one.
The task of CON (my opponent) is to demonstrate that 0.999... is not exactly equal to one.

All my opponent has presented is variations of the phrase 'It doesn't make sense', regardless of the fact that I have shown mathematically that it does make sense. As a guess, I would suggest that my opponent fails to recognise the notion of 0.999... it is not a finite number, it is infinite, it has no end at all. The statement 'it will infinitely be less than one' doesn't make sense because there is no end to this recurring decimal, it does not stop at one particular 9. If it did, then indeed I would be mistaken in my proposal that (as an example) 0.999 is equal to one. Allow me to demonstrate with my previous example, although this time showing why this can only work with recurring nines.

x = 0.999
10x = 9.99
10x - x = 9.99 - x
9x = 8.991
x = 0.999

And I am sure from here you can see that indeed 0.999 =/= 1, the same is true for any finite number (except 1 lol), however for infinite recurring decimals it is indeed true that 0.999... is exactly equal to 1. To further expand on my point, allow me to show another example of what I just did.

x = 0.9999999
10x = 9.999999
10x - x = 9.999999 - x
9x = 8.9999991
x = 0.9999999

You'll have to forgive me if I forgot a few nines (it was meant to be 7 nines), but the point should be clear by now. The case of 0.999... = 1 is only true for 0.999...

Not only that, but the proof also doesn't work for other recurring decimals such as 0.888...

x = 0.888...
10x = 8.888...
10x - x = 8.888... - x
9x = 8
x = 8/9

Only for 0.999... does it equal exactly 1.

Now, allow me to present a simpler proof of the resolution. I'll do my best to explain each step.

1/3 = 0.333... [Any calculator can confirm this]
3*(1/3) = 3*(0.333...) [brackets added for ease of viewing, both sides are multiplied by three]
3/3 = 0.999... [I bet you can see where this is going]
1 = 0.999... [TADAAAAAA]

This proof is much easier for our less mathematically minded voting audience, essentially what it is saying is that one third equals 0.3 recurring, when both sides are multiplied by three, the proof yields 1 = 0.999... some people may be wondering how I can simply multiply an infinitely recurring decimal by a finite number three. The answer is simple, as the 3's in 0.333... never actually end, the multiplication simply consists of making them all nines, of course if it was a finite number I could not do this proof either. It would fail at the very first step.

1/3 = 0.333 [WRONG!]

The same proof works for 1/9, for instance

1/9 = 0.111...
9*(1/9) = 9*(0.111...)
9/9 = 0.999...
1 = 0.999...

Now my opponent talks bout how 'math isn't perfect' and indeed there are still many paradoxes to be solved, however unless my opponent wishes to disprove rudimentary reasoning and the very basic algebraic processes which are the framework of most mathematical disciplines, then I suggest he attempt to highlight my arithmatic ineptitude.

Ladies and Gentlemen, I have thoroughly acheived by burden. The only reasonable vote is PRO. I'll be happy to answer any questions by the voting audience in the comments section.

Thank you

as I stated before, mathematics are full of error. it always has to do with tricking the system. by using the equation, 10x-x, my opponent has tricked the system. it is an illusion saying that it is exactly equal to 1, but all you need is common sense to figure out that it isn't.

my opponent tried to confuse you by changing the eqation on you when he mentioned .888 is not equal to 1, but if you use the equation exactly as my opponent did....

x = .999
10x = 9.999
(10x)-(x) = 9
9 is now a whole number, and is an equivalent of one.

x = .888
10x = 8.888
(10x)-(x) = 8
8 is now a whole number, and is an equivalent of one.

x = .777
10x = 7.777
(10x)-(x) = 7
7 is now a whole number, and is an equivalent of one.

voters, my opponent is trying to trick you. he found the mathematic error, and he's trying to turn it on you guys. use your common sense is all I have to say. logically, the correct side to this is that .999... is NOT exactly equal to 1.

if you were to try to use any other equation to make .999 reach 1, it is impossible. please vote in negation, this has been a fun topic. THANKS!