0.999... is NOT equal to 1
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On my previous debate:
I definitely proved that 0.999 does = 1. The most compelling proof of that was:
X = 0.999...10x = 9.999...10x - x = 9.999... - 0.999...9x = 9X = 9/9 = 1
To prove that the conclusion is in fact wrong, i will repeat the same arithmetic on another number: ...999.0.
X = ...999.0
10x = ...9990.0
X - 10x = ...999.0 - ...9990.0
-9x = 9
X = 9/-9 = -1
Clearly something went wrong because even a single 9 before the decimal point is greater then 0, forget about an infinity of 9s. A negative number is an absurd conclusion, thus the argument that they are equal is reduced to absurdity.
This is interesting.
First of all, I want to thank you because you proved 0.999... = 1 for me. So there is no need to give some proof other than this.
But, in second "proof" you made mistake even before you started calculation. You said you will use same arithmetic on number ...999.0. And that is the mistake: number like this does not exist. Because if you said that number is ...999 then it is infinite number-there are infinite period of 9s after 0. and you can't just put 0 after infinite period of 9s otherwise it wouldn't be infinite... It isn't even a number. It's same as you wrote 0.999...0 - number like that does not exist.
Hope this proves my point.
Your welcome, it wasn't something I was trying to hide.
However, it is contradictory to say that an infinite amount of 9s before the decimal is not valid, while accepting a number with infinite 9s after the decimal.
if ...999.0 does not exit, then neither does 0.999..., which invalidates the original proof of 0.999... = 1. Thank you very much. Please vote PRO! :)
It is contradictory to say that neither of our proofs are true and because of that one side or other should win. You tried to go off topic.
So, to review this shortly and clearly:
1) 0.999... IS periodic infinite number(check it anywhere, ask teacher in elementary school, if you aren't ashamed)
2) 0.999...0 (what you tried to calculate) IS NOT an infinite number like we said, because it has end-that's 0.
Don't vote for con, but VOTE for common sense. ;)
1. Ending in zero doesnt make it any less equal to infinity. It has infinite 9s in front of it.
2. I was not trying to prove that ...999.0 = -1. I was trying to prove, as per topic, that 0.999... does NOT =1. Specifically by invalidating the method used to prove that it does and settle a long fought debate in mathematics.
1) You said, I quote: "Ending in zero doesnt make it any less equal to infinity." I am pretty sure that everyone reading this debate at the moment will agree with me that, if something has ENDING, then it is NOT INFINITE.
2) Objection to your second statement: You were trying to prove that 0.999... is not 1 BY proving that ...999.0 is =-1. So, if your method isnt valid and clear, conclusion from it cannot be any more valid or clear. :)
1. In numbers, "ends in" refers to the smallest part of a number, the singles spot. Thus 1,000,009 "ends in" a 9. So having a zero in the last and smallest position doesnt change the infinite 9s before it. Hundreds, millions, billions, and on to infinity.
I trully do not understand the confusion here. Your argument revolving around "ends in" is essentially a play on words.
2. My opening statement, where i did the initial =-1 equation concluded with a declaration that both results are absurd. My arguments involved how similar the numbers and methods are, and I highlighted how if either one is invalid, both must be invalid.
Ill let #2 also be my closing statement.
As a bonus, i will show method to this madness with one more number:
X = ...999.999...
10x = ...999.999...
10x - x = ...999.999... - ...999.999...
9x = 0
X = 0
Which again seems absurd... until you realize that
...999.0 = -1
0.999... = 1
...999.999... = ...999.0 + 0.999...
...999.999... = -1 + 1 = 0
At least the insane equations work together :)
You found the truth my friend, we all live in matrix and all world around you is a simulation. Maybe this could be a topic for some other debate...
Seriously now, I wanted to give myself some logical answer to this "problem" and I did some research. And even basic math with infinity is just...well,undefined. So, for example:
infinity+ 1= infinity, but subtracting infinity from infinity, well we could call it 'not-a-number-ness', because subtracting from infinity doesnt have a definite result,so your calculations fall short because of this. You tried to subtract infinity, and I respect that try, minds like you could change a world for better, just focus on something more practical. :))
After all, many big mathematician brains have been thinking about this long before us, so if it is consensus, it is consensus because of these things I mentioned above,and many others for sure.
We really live in a world full of absurds and anomalies, but thank you for high-quality debate.
Hope to see you in some next debates.
P.S. This could be named a 'tie' but let the votes prevail. :)