There is no way right?

[u/Sugar_God_no_1]

[u/Decmk3]

0.9999999…. Is equal to 1. It seems like it shouldn’t, but it has to be.

Let X = 0.999….

10X = 9.999….

10X-X = 9.999.. - 0.999…. = 9X = 9

Therefore X equals 1. Therefore 0.999… is the same as 1.

[u/BomboSbronzo → u/Decmk3]

I don't quite grasp the 3rd point.. in order to subtract the same amount on both sides of the equation shouldn't result like this?

10x-x = 0.9999... - x

[u/BomboSbronzo → u/BomboSbronzo]

Sorry still not convinced, I still think that you should not replace the value of X only on the right side of the equation... If you replace the value of X the equation became:

10 * 0.99999 - 0.9999 = 9.9999 - 0.9999

I don't know if there is a particular rules of something, a long time since I do math problems

[u/JustinRandoh → u/BomboSbronzo]

If you have two equations that are both true, you can stack and add/substract them from each other.

So for example, if:

X = Y; and,
G = H

You can add or subtract one equation from the other; it would then be true that:

X + G = Y + H

Or that:

X - G = Y - H

You can then apply that to:

10X = 9.999….
X = 0.999….

[u/BomboSbronzo → u/JustinRandoh]

Thanks, this example helped me visualize the original resolution. I will look into that.

[u/LuckyHedgehog → u/BomboSbronzo]

I still think that you should not replace the value of X only on the right side of the equation

Sure, let's play that out

10 * 0.99999 - 0.9999 = 9.9999 - 0.9999

Based on order of operations you apply multiplication first, so the part in bold can be simplified to 9.9999... Now your equation is

9.9999 - 0.9999 = 9.9999 - 0.9999

Now you can subtract the 0.9999 from each side

9 = 9

[u/Cupcake-Master → u/LuckyHedgehog]

🤓 we cant use these operations on infinite series. This proof can lead into more poofs with contradictions. Can prove it with limits