I'm looking for the mistake I made, but I can't find it.
1/9=0.11111111.....
2/9=0.222222222...
3/9=1/3=0.33333333333...
4/9=0.4444444444...
5/9=0.555555...
6/9=2/3=0.66666666666666...
7/9=0.7777777777777777...
8/9=0.888888888888888888...
SO
9/9=0.99999999999999...=1
0.9999999999999999...=1
AND
1-0.9=0.1
1-0.99=0.01
1-0.99999=0.00001
BUT
1-1=0
So
0.0000000...01=0


adding a zero to an equation does not change it, SO
2+3=2+3+0
and multiplying zero by any number, including infinity, does not affect the zero, SO
2+3=2+3+0=2+3+0*∞.
THEREFORE
2+3=2+3+0=2+3+0*∞=2+3+0.0000...01*∞=2+3+0.9999999...=2+3+1=6
2+3========================================================6
2+3=6

This is not evaluatable. You have a 1 following an infinite number of zeroes after the decimal point, and you have infinity. This can equal anything, depending on the relative sizes of the infinities.

Exactly. You then, in the next step, set it equal to 0.9999999999...99.

Edit: It has come to my attention that this post is unclear. I am noting this not as the correct step, but as the step that is in error, as 0=1 is false.

In addition, you are multiplying by infinity. You can't do that because it isn't an actual number. You may like this.

Fine...suppose I multiply by 999999999999999...

That would be infinity. Infinity times an infinitesimal (0.00000...01) is by nature undefined, as the relative scales of the infinities involved could make it anything.

Same thing if it's an infinite series:

No, it should be:
=1+(-1+1)+(-1+1)+(-1+1)+...-1=
=1+0+0+0+...-1=0

No, that doesn't make any sense. Neither does. The first doesn't make sense because it doesn't make sense to add or subtract from a divergent series. The second doesn't work because you're presupposing an end to an infinite series. Stop making my math squeal in pain.

...I was trying to show an example of how not to add to the "end" of a series. Here we add something to the "end" of a divergent series. That's even worse than adding it to the end of a convergent series, as in 0.0...01.

I never said that the premise made any sense.



I never said that my version was right either, only that if one was going to do one as idiotic as that, that's how it would work. Why?

You start with something like:
1+(-1+1)+(-1+1)+(-1+1)-1
then extend it and take that "limit" to infinity. No, it is not rigorous math. I never claimed it to be. However, it does make sense enough to show why it's closer to being right than the original.

PS: I like how you ignore how the OP "presupposes an end" to an infinitely long number, namely, 0.0000...01. If mine makes your math squeal in pain, that should have long ago. Get your math squealing priorities straight.

No, that thinking might fly in Philosophy, but not in math. You can't using the excuse of not claiming something is rigorous, yet thinking it is still "closer to right" than something else. There are no personal interpretations of math, there is only that which can be proved rigorously; anything else is gibberish.

Why do you guys keep ignoring the fact that this comes after the acknowledgment that doing any such thing to an infinite series is wacked? It never was "true rigorous" math. It, from the beginning, was a philosophical point showing that in such a bizarro world the series would still equal zero.

Plus anyway, my point about ignoring the 0.0000...01 (which is most certainly not rigorous by your definition) was rather important, don't ignore it.

Trust me, it all makes me squeal in pain. I just expected better of you Deck. :'(

I was talking with eofpi about this thread, and came to the conclusion that it was more a difference in mental representation than actually being wrong. (And me being bad at explaining what I mean, see my note in my first post in this thread.) My main point with the series thing was not that there was an end (as there is not, I never claimed there to be), but that a -1 was dropped.

If it upsets you enough, then by all means, replace what I said with:
=1+(-1+1)+(-1+1)+(-1+1)+...-1+(1-1)+(1-1)...=
=1+0+0+0+...-1+0+0...=0
In my mind, so long as two mental representations get the same results, there's not that much of a problem.

Hello, me again. I got into an argument with my math teacher, about the part where I said that 0.(9)=1
I need proof of this before tomorrow
EDIT
Evening...
I'll check tomorrow morning
I don't know if this works:
1/3=0.333333...|*3
1=0.999999999...

You say that 999999...=∞
I should multiply by 0.99999.../0.00000...01
BUT
0.000..001=1/10^∞
So 0.999999.../0.0000...01=0.99999.../(1/10^∞)=0.9999999*10^∞=999999...=∞
0.00000000000000...01*∞=0.999999...

...no?

We keep telling you, that's wrong. If you are adding 0 to something, its value does not change. If you add something that may as well be zero (an infinitesimal), then you multiply said infinitesimal by infinity, you broke the problem. Undefined is undefined is undefined is undefined.

Furthermore, you're pretending that I could take 5 + 1 = 6 and multiply the 1 by something. You cannot do that. Any operation you do to one side you must do to the other, with few exceptions. Said exceptions are multiplying by 1 (infinity is certainly not 1), adding 0, or other things that do not change the veracity of the equation (such as adding one equation to another.)

Notice, I added 0*x which equals 0
so I added zero pretty much
also, is my proof that 0,9999...=1 true?
That is what I really need.

0*x=0 is true.
0.0000...01*x=0 is true (Using the infinitesimal definition and shorthand, 'cause I'm too lazy to use limits.)
0*infinity=0 is true.
0.0000...01*infinity=0 is NOT true. *This* is what you used.



I don't think that that is possible to prove without calculus, at least in a rigorous fashion.

but will my math teacher accept it?

Rule of thumb: If you're not sure if a teacher will accept something, ask them. Other people aren't grading it.

Furthermore, the subtext for the math/science forum clearly states: "We won't do your homework for you."

As I stated before, this is not homework but an argument. It turns out my math teacher completely forgot about it and I went to all this trouble (my previous post, and the one before that, I'm not discouraging further discussion) for nothing.

Between every two rational numbers there exists an irrational number.
It is impossible to construct a number between .99999... and 1
Therefore, they must be the same number.

That's an interesting way to go about it that I didn't think of, though. Related to the calc-proof, but still different. Interesting indeed.