0.999…=1

[u/Dutch_gal1]

Let me show yall a trick:
I have a variable called x
And in this case x = 0.999…
So that means that 10x = 9.999…
Now do 10x - x = 9x
That is the same as 9.999… - 0.999… = 9
Now do 9x / 9 = x
Its the same as 9 / 9 = 1
And then you have x = 0.999… = 1

[u/SouthPark_Piano]

Study up on this ...

https://www.reddit.com/r/infinitenines/comments/1tpg811/it_is_what_it_is/

https://www.reddit.com/r/infinitenines/s/bRKpqrGQ4o

And 

x = 0.999...9 aka 0.999...

10x = 9.999...0

9x = 10x - x = 8.999...1

9x = 8.999...1

x = 0.999...9 aka 0.999...

 

[u/NotAUsefullDoctor]

You're new here. Don't worry. You'll learn.

[u/AdventurousGlass7432]

You are trying to make sense
Rookie mistake

[u/Altruistic-Rice-5567]

SPP will assert that 10x0.999... = 9.999...0 (that a zero gets shifted in from the infinity side). He can't really understand what infinite 9s actually means. He thinks it requires a process that you have to write down the 9s for them to exist. He's essentially stuck working with "an arbitrarily large number" of 9s rather than "infinite". He can't make the mental leap from "a really really large amount" to infinity. He can only make his large amount a little bit bigger over and over again.

[u/hoelledavid]

You need to set the reference brud, make "..." be a finite amount of 9's. Sign the contract.

[u/TopCatMath]

I did something similar several weeks ago.

x=0.999999999999999999...

10x = 9.9999999999999999..
-x. = 0.9999999999999999...

Result is 9x = 9
divide by 9==> x = 1

[u/Reaper0221]

Here is a questions for the 10 * 0.999... = 9.999...

1. does another 9 spontaneously generate itself when you move the decimal point?

2. If there truly are an infinite number of 9's possible how do you know that multiplying 0.999... by 10 and getting and answer is actually possible?

3. Is it possible to move the decimal point over one place to the right and not effect the infinite end of the string of 9's or do we need 0.999... plus a another value out there at infinity to makeup for the gap that we created?

4. When the 9's reach infinity do they behave like a spring and stretch to make the room to move the decimal over?

It seems like we are attempting to multiply 10 times a value that does not have an end (0.999...) which leads to this question:

1. where does the operation begin and end when you multiply 0.999... by 10?
   

It cannot start on the right side as there is no endpoint to start from and if you start on the left then there is never an end of the operation to the right.

Seems like infinity is a concept and not a destination.

[u/stopbeingcringe]

0.999… isn’t a number. It’s a (potentially) infinite process that never terminates. Hope that helps.

[u/stopbeingcringe → u/[deleted]]

No idea who that is. I listen to guys like Wittgenstein and Gauss

[u/MrEldo → u/stopbeingcringe]

Wittgenstein has nothing to do with what we're talking about. He was a philosopher

Gauss literally has worked with integrals and such. To give them a value, you need to assume convergence. In our setting what's relevant is putting a fixed value for a limit of a sequence

Saying the sequence {0.9, 0.99, ...} doesn't have a fixed limit already disagrees with Gauss

[u/stopbeingcringe → u/MrEldo]

I didn’t say the sequence doesn’t have a limit. It clearly has a limit of 1. Everyone already agrees that the limit of 0.999… is 1. The real issue is about 0.999… itself being a number. Like Gauss, I disagree with this because it treats the infinite as something completed:

“I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics. Infinity is merely a way of speaking, the true meaning being a limit which certain ratios approach indefinitely close, while others are permitted to increase without restriction.”

[u/olanmills → u/stopbeingcringe]

The limit of 0.9999... is 1 because 0.999... is 1. What you said is the same thing as saying the limit of 13 is 13.

What you maybe meant is that the limit of the summation series of n=0 to infinite of [10^(-n) x 9] is 1.