The ....... after the 9's does make it a whole number. It's a quirk of the way we write numbers.

Infinite numbers are an understandably complicated concept to master. The concept of infinity is probably the first time in which even a competent math student won't be able to rely on intuition to help derive answers. Like many things going forward, infinity is just one of those things you need to trust your math with to get the right answer.

@jc .5 is definitely the same as .500000...

@Diplomat, fuzzyhartle is not the person you should be looking at for moth advice. He has proven himself to not understand simple concepts of diplomacy, he thinks that the printing press was the beginning of written language, and you have people in this thread like uclabb who are pretty advanced mathematicians. You shouldn't be listening to any argument in a math discussion that starts with "be simple no math."

@Diplo, zultar's excellent proof should end the discussion.

@jc

Mathematically, 0.5:=0.50000.

Now, in science, 0.50000 would represent a measurement with higher precision than 0.5, but that is not what this conversation is about.

i suppose if you are simple, and don't do any math, you will see that in actually fact, the two written things here '1' and '0.99999...' are not the same thing, because they have a different number of characters.

It does takes some math i'm afraid to understand that they represent the same number.

and just think about what 0.5000..... would mean. Infinite precision?!

Well then we'll just say 0.9999... = 1.000... problem solved

yes, 0.5 is equal to 0.50000 but one cannot simply substitute one for another because 0.5000 has more significant figures and contributes to more precision.

mathematically 0.50000000 is the same thing as 0.5

Each is a perfectly precise number, not representing a measurement which may be less than precise.

there is no distinction or difference between the two, if i was doing physics, i agree, i would use one over the other to represent the difference in precision, but this is not what we're doing in this thread.

I should write a book called "Be simple, no math: Why Polandball cannot into space".

Another point, Diplo. You said you don't want limits, but a question here would be, what do decimal numbers _mean_? How is the notation actually defined? We write down numbers and don't think about it much, but there must be some way to give actual meaning to the notation?

Simply, the decimal number .(a_1)(a_2)(a_3)... means the sum from 1 to infinity of (a_i)*10^(-i). That's what it MEANS. (If the number terminates after a_k, then we take a_j = 0 for j>k). This is the only way to give meaning to an infinite decimal in the first place.

SO. What is 0.99999.....? It's the sum from n = 1 to infinity of (9/10)*10^(-n). That's just a simple geometric series, and we have a simple formula for the sum: (9/10) / (1 - 1/10) = (9/10)/(9/10) = 1.

If you don't agree, then it just means you have a different definition of decimal number in mind, but unfortunately, whatever it may be, it won't agree with the standard of what people mean by such, and it won't be useful in expressing other numbers.

Zultar is as always, completely right on this mathematics topic.

In mathematics no-one would write 0.50000000, because the 7 zeros behind the 5 are all meaningless. To actually write the zeros would imply that the answer is only accurate to 8 significant figures, which could happen with some mathematical methods where an exact answer is unachievable. (say finding the root of a 5th-degree polynomial with the binary method)

"hahahaha
so if 20=1/3 so 1=60 60/3=3/3=20*3=3x=1/1?"

This is all I can think of:

http://i.imgur.com/psUnc.gif

For the wikipedia fanboy: http://en.wikipedia.org/wiki/0.999...

Also, I like the Big D nickname. Bravo

lawls abge

OP is trolling

Big D isn't a nickname, it's just the way Big D is. We can't help responding to Big D even though he is always messing with us. That's how big Big D is. I knew it in the moment I saw his first post here. He was Big D. He was born that way.

RIP Big D

OP is not trolling - when I was 11 years old I thought the same way he did I insisted that
.999 repeating < 1

because I thought math was just fudging for consistency's sake.

For the record I do not think there is such a thing as an actual, physically manifested infinity. However it is useful as a mathematical concept, which is something I have come to accept since I turned 12.

Or since I turned 11.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

I can't believe there has been this many posts on this topic. No further post was necessary after Zultar's simple and elegant proof. (I like ulytau's too I haven't seen that before!)

At YJ, really? You haven't seen that second explanation?
That's the explanation I gave to my eighth grade students in Algebra I the first time they ask the question. Then we proceed to prove it algebraically.

I find it interesting that 4/30 main threads on this Diplomacy site are math/science related.

"Finally, FINALLY I SAW A NO-MATH EQUATION WITH = !!! NEVER AGAIN WILL EQUATIONS MAKE NUMBERS EQUAL BY USING EQUATIONS WITH EQUALITY SIGN!!! FINALLY A SIMPLER MATH FOR SIMPLER UNIVERSE!!!"

ahahahahaaa. Preach on, brother.

And thanks for the complement. :)

lol zultar I'm a physicist. I'm interested in math only so far as it's necessary for what I do. I will not be able to recall your (or uly's) proof tomorrow, it is enough for me to remember that .99999 = 1.

But you can't do string theory or quantum mechanics without math.
The boundary between math and physics or even science/logic and metaphysics gets blurry when you look at the universe in the most fundamental way.

"I'm interested in math only so far as it's necessary for what I do." I think this is pretty clear. : )

@YJ

When did you become a physicist? I thought you were a biochemist or something along those lines.

I'm not saying math is useless. Far from it. I'm just saying save it for the mathemeticians :P

abge I'm a grad student in medical physics. Been in physics for 8 or 9 years now.

Oh, I must have had you confused with someone else then.

What do you do for medical physics? Things like non-evasive testing?