I remember a few weeks (month?) ago there was a discussion about how 0.99999' = 1. Well, for all you non-believers:



Can't be any more simple then that.

Except that you don't show any proof for 900x = 900... Anyways this was shown correctly in the other thread but... nt

1000x - 100x = x(1000 - 100) (factor out the x)
x(1000 - 100) = x(900) = 900x (subtraction)
900x / 900 = x (division)

Updated the original proof to have a subtraction sign for mikus.

It was funny. There were a couple morons having a discussion in one of my CS courses today. Some guy had the proof you showed above, and all the others were like "Psh, that's crap!" And all this crap. I couln't believe my ears. I just wanted to give each and every one of them the backhand, but instead, I left disgusted and went to sulk in the corner.

Heh. Yeah, I posted that I think, in the previous thread.

Fun proof though. I've annoyed a great many people with it..

"*proof*"
"That can't be right! See here, erm.. oh.. wait. Well, s***."

iirc, there's some fundamental flaw with that proof, but I can't remember what. But interesting nonetheless. Also seen it as

1/3=.333333333333333(continuous)
2/3=.666666666666666(continuous)

1/3+2/3=1
.33333333333333(continuous)+.66666666(continuous)= .9999999(continuous)

therefore,
1=.9999999(continuous)

Something to that effect.

I am still somewhat amused by people failing to properly understand the basic concepts of calculus (such as infinity), though it's annoying me that their ignorance is showing the potential of spreading.

I'd also like to ask just how many of you actually write any programs.

I agree. People like you are amusing. You really should learn something about the subject before running your mouth.

And forgive me if I question the programming experience of someone who claims that FPU-less computers crash when dividing 1 by 3.

Subtracting infinite series... Rofl.

That's what I was thinking but I didn't want to say it in case it was wrong.

I'm not positive on it, but fundamentally I would think that infinite series subtraction would be like subtracting infinity from infinity, which yields an indeterminant answer.

Infinity is a funny thing, but it strikes me that if .999 - .999 = 0, then the same should be true for any number of 9s when the number of nines of each side of the - is the same. Even an infinite amount. It's the same way you can prove that the set of rational numbers is not countable, but the set of all integers is.

Here's the same proof, made a little bit simpler, with pretty unicode overlines:

Same size? I'm pretty sure 1 inifinite fits all...

.. I think you're missing the point.

We /know/ that .999... doesn't equal 1. But it's fun to watch other people get frustrated because of a fundamentally wrong equation.

What's fundamentally wrong about it?

There's countably infinite and uncountably infinite, depending on how the sets can map to one another. The set {0,1...infinity} is infinite and also the same size as the set {1,2...infinity} because the second set can be defined in terms of the first (very loose definition and example).

Hotel Infinity is fully booked, someone arrives wanting a room, obviously there is a problem which is quickly resolved by giving all exisiting customers a room with the number one greater than they one they are currently in.

Hotel Infinity is fully booked, an infinite number of people arrive wanting to move in, obviously moving everyone up an infinite number of room numbers is just silly. So instead, every existing customer is given a room with the number double that of their current room leaving space for the new customers.

Isn't infinity fun?

Every real number is defined by an infinite sequence or series. But if you want to stick with ones that have infinite digits after the decimal point, consider pi or e. Do you "rofl" every time you write 3*pi or pi - e?

rofl, a group of teenagers don't know advanced calculus 1700, what losers. :rolleyes:[/end sarcasm]

Rather than saying "giving infinity a value," it's perhaps a bit
clearer to say, "giving the concept of a limit of an infinite sequence
of numbers a value."

.9 is not 1; neither is .999, nor .9999999999. In fact if you stop the
expansion of 9s at any finite point, the fraction you have (like .9999
= 9999/10000) is never equal to 1. But each time you add a 9, the
error is less. In fact, with each 9, the error is ten times smaller.

You can show (using calculus or other methods) that with a large
enough number of 9s in the expansion, you can get arbitrarily close to
1, and here's the key:

THERE IS NO OTHER NUMBER THAT THE SEQUENCE GETS ARBITRARILY CLOSE TO.

Thus, if you are going to assign a value to .9999... (going on
forever), the only sensible value is 1.

There is nothing special about .999... The idea that 1/3 = .3333...
is the same. None of .3, .33, .333333, etc. is exactly equal to 1/3,
but with each 3 added, the fraction is closer than the previous
approximation. In addition, 1/3 is the ONLY number that the series
gets arbitrarily close to.

And it doesn't limit itself to single repeated decimals. When we say:

1/7 = .142857142857142857...

none of the finite parts of the decimal is equal to 1/7; it's just
that the more you add, the closer you get to 1/7, and in addition, 1/7
is the UNIQUE number that they all get closer to.

Finally, you can show for all such examples that doing the arithmetic
on the series produces "reasonable" results:

Since:

1/3 = .333333...
2/3 = .666666...

1/3 + 2/3 = .999999... = 1.

By the way, there is nothing special about 1 as being a non-unique
decimal expansion. Here are a couple of others:

2 = 1.9999...
3.71 = 3.709999999...
2.778 = 2.77799999999999...

...and the person who says you're trying to show that 1 = 1/infinity
is wrong. *

>.>
<.<
.
.
.
.
.
.
*I didn't write that.

Hahah I know the Taylor Series Expansion of Sine and Cosine and you dont! Na na na

Yes I do! :p I know the Taylor series for e also :p

You can't perform precise calculations with infinity/repeating numbers without estimating. This is why I disagree with this proof.

If all the decimals can't fit in 8 bytes, don't bother.

The math is perfectly valid, but it's more of an example than a proof.

A real proof is to simply define the Reals with Cauchy sequences of rationals and then note that the sequences which define .999... and 1 are equivalent. Or you can do it with Dedekind cuts, but they're more complicated.

In any case, any definition of the reals demands that .999... and 1 be equal.

...what?

[EDIT: Sigh, don't want to get banned (I would have easily been permabanned). He just irritates me so much.. ]

if 0.9999.... is one, does 0.666666... = 0.7?

But isn't 2/3 = 0.666666...
and 0.7 = 7/10

now if 0.666666...=0.7 then 2/3 = 7/10.

and the whole fabric of maths collapses... :p

increase 0.333333 by 0.000001 and you get 0.333334, not 0.4
increase 0.999999 by 0.000001 and you get 1.000000.

increase 0.666666 by 0.000001 and you get 0.666667, not 0.7.

As 0.999... tends to it's infinitieth decimal place, the amount required to reach one becomes infinitely small, when it reaches infinity the difference becomes zero, thereby making 0.999... equal to 1.

Of course.......

>.>

Pi is exactly three!!!!

Since it's not precise, I don't believe it.

How is anything in this thread not precise?

|

You can't argue with numbers...

I think above posters are quite correct when saying that you can't perform operations on infinity.
For example, there is are an infinite number of integers, and also an infinite number of positive integers. How can you subtract one from the other and expect to get 0?

Infinity is not a number, it's a concept.

...but that's just me.

And since it never reaches infinite, it's never equal to one.
GG.

Of course you can prove it mathematically, just like you can prove 1=2. The problem lies in logic, 1 != 0.999...

c/o Fred Richman...an actual educattor http://www.math.fau.edu/Richman/html/999.htm



Also: This


or maybe this...

I retract that. Yo do not even need 9th grade algebra to understand the logic in these simple steps. So either show us your thesis that you are submitting to MIT to get your PHd in Math disproving this fact or...shut up.

What some people on this thread fail to realize is that this is not philosophical in nature. It's not up for debate. It's a fact that 0.999... is equal to 1. If you don't understand how, then learn. Google will aid in this. If you wish to debate, don't, because you're wrong.