Sythe Users: What Do They Know? Do They Know Things?? Lets Find Out! #7

Question, is that 0.999... repeating, as in never ending?

 

yes, 0,9 followed by an infinite amount of 9.

that's why he is able to show that 0.9 = 1, if there isn't an infinite amount of 9s, it isn't equal to 1.

for example,

0,999 != 1

0.999 = X

10X = 9.99

10X - X = 9.99 - .999 = 8.991

9X = 8.991 => X = 0.999 != 1

 

Not sure how you want to go about this,

in the above picture, Y and 10Y both are equal to infinity because this is a geometric series whos ratio is greater than 1

 

So then how exactly can you claim the following (pardon my poor notation):

Y = 0.999...

10Y = 10 * (0.999...)

10Y = ...99990

While the basic principle makes sense, isn't that effectively giving infinity an endpoint, which you cannot do? That's saying that where the 0 now is, that was the end of the infinitely repeating 9s. How can there be an end to that?

 

Y is ...999 where the 9s extend infinitely to the left

 

...99999 is an infinite amount of 9s to the left of the decimal.

if you'd like to know more about such things, i believe this could be useful

https://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel

 

y = ∞
y + 1 = ∞
y - ∞ = ∞

there.

edit: Y is infinity. Therefore Y is all numbers simultaneously.

 

you fail so bad, infinity is not all numbers simultaneously

if so you could say

∞ = 2

∞ = 4

∞ = -74

and then you could say that 2 = -74 = ∞

see how that doesn't work ?

 

There isn't a single scenario where ...999999 infinite 9's are generated unless they're in the decimals. If thats what you mean, then .9 repeated.

it doesn't equal -1, but -1.1 repeated.

 

.9999999... = 1

not -1.1

 

You're right, it doesn't work. That's because infinity is a concept and doesn't exist in reality. Therefore it cannot be calculated logically.

Edit: The proof itself already uses that logic that you are professing against. It claims that ...999999 = -1

It does not work both ways because an infinite fraction is not an infinite number and is not comparable.

 

huh ... an infinite fraction is an infinite number ... it's 0,9 followed by an infinite amount of 9s.

the proof doesn't assert that infinity = -1 or 1,

it just uses algebra to get rid of the concept of infinity

X = 0.9999...

10X = 9.99999...

10X - X = 9.9999... - 0.99999....

9X = 9 => X = 1

 

And it arrives at the conclusion that -1 = 9999999 proving conventional mathematics is inadequate at handling infinite concepts. I'll agree that even infinite decimals are infinite since using the same mathematics, one is still forced to round the number to arrive at a solution, a technically incorrect one at that.

Edit: Even the original problem proposes 9.99999... - .99999... = 9. This is incorrect. This problem could never be solved because it would be subtracting infinitely meaning it would never arrive at a solution. Just in the sense that ∞ - ∞ = ∞. Infinity will always be infinity no matter what you give or take from it.

 

savage

 

Would you say, instead, that in regards to 9.99999... - .99999... = 1 it would not equal 1, not because you subtract infinitely, but because no matter how close it gets, it never technically reaches the value of 1. So doctor butt is applying the same logic to a different equation to prove it is wrong?

 

Why can't we say then that 0.999... + x = 1 has the solution x = 0.000...1?

 

Using the logic of my previous answer, I would say that 0.000...1 = 0 because, in having an infinite amount of zeros before the 1, it is infinitely small and would only contain a 1 if it had a finite number of zeros.

 

yeah idk, don't understand how we can't say that ...999+1 = ...000 = 0 because there isn't a position that a leading 1 can occupy


final thoughts:

...999 represented as a geometric series does not converge. We can't say that ...999 is equal to -1, just that it behaves like -1. We can maybe think of it in terms of modular arithmetics where numbers cycle through equivalence to 0. Just like how for certain odometers 10^6 (or whatever analog odometers go up to) is equivalent 0 as 999999+1=0 --> 999999=-1. Seeing the same thing for ...999 is the result of having infinity equivalent to 0 somehow??