0.999999[r] = 1

[blahblah99]

Originally posted by: futuristicmonkey
sao123, you are an idiot. The reason I didn't put the repeating sign on there is because if you did multiply .3333333333[r] by 3, all the threes would be turned into nines.

To Repent, You Must:
[ ] Give up your AOL Internet account
[ ] Bust up your modem with a hammer and eat it
[ ] Jump into a bathtub while holding your monitor
[ ] Actually post something relevant
[ ] Be my love slave
[X] Apologize to everybody on this forum for wasting space
[ ] Go stand in the middle of an intersection
[ ] Other: Eat your calculus book
[X] STFU and get a life, then go commit suicide

Go take a piece of paper and divide 3 into 1, and repeat until you run out of paper space. Then stick foot in mouth.

 

[futuristicmonkey]

I understand infinity. But, there is no such thing as 1/3 of 10 - that we can write down with numbers. Sure, we can draw a circle and divide it into 3 equal pieces, but you can't write down 1/3 of 10 using numbers. It doesn't matter how many 3's you put onto that number - it'll never be exactly 1/3 of 10. Sure, it'll be close, damn close, so close that we wouldn't know one from the other, if they were measurements (in inches, centimeters - whatever), and we were looking at them with our eyes. It'll be close, but not exactly 1/3.

If .99999999[r] did = 1, wouldn't it then be called 1? Think about it, and don't flame me in the process - this isn't personal.

Oh, and i forgot, sao, Peter, blahblah99, if you're all so smart, can you tell me what the smallest number there is, is?

 

[Peter]

You do NOT understand infinity. From your 2nd sentence, you have clearly demonstrated this.

 

[futuristicmonkey]

Originally posted by: Peter
You do NOT understand infinity. From your 2nd sentence, you have clearly demonstrated this.

What is it that I dont understand? That it goes on forever?

 

[Peter]

You say you understand what an infinitely long number is, and in the following sentences blurb on and on and on about how finite numbers approach the infinite one and yet never reach it - and yet fail to see that

EXACTLY THAT IS THE FVCKING POINT ABOUT IT.

3 * 0.33333 is 0.99999 is most obviously not = 1, no matter how large a finite number of digits you use.

3 * 0.33333[r] _is_ 0.99999[r] _is_ 1, however. This is because these are infinitely extending numbers.

 

[futuristicmonkey]

Originally posted by: Peter
You say you understand what an infinitely long number is, and in the following sentences blurb on and on and on about how finite numbers approach the infinite one and yet never reach it - and yet fail to see that

EXACTLY THAT IS THE FVCKING POINT ABOUT IT.

3 * 0.33333 is 0.99999 is most obviously not = 1, no matter how large a finite number of digits you use.

3 * 0.33333[r] _is_ 0.99999[r] _is_ 1, however. This is because these are infinitely extending numbers.

Your logic is flawed. I can just say that if .999999[r] did = 1, then it wouldn't be called .999999[r] - it would be called 1. And, you haven't answered my question yet. What is the smallest number?

 

[Cogman]

Ahh, but that has been answered, The smallest number is negitive infinity. futuristicmonkey I believe that your logic is a bit flawed.

You have recieved many proofs the .9999[r] = 1, so now I ask you, Prove that it doesnt. simply saying that .999[r] != 1 does not work either, that is like saying that (-1)^(1/2) !- i.

I had a math teacher explain it something like this. If you take a basket ball court, and travel half way, then travel half that distance, And so on, that is you do that for an infinit amount of time, you would reach the other side. But if you ever stopped traveling you would never make it to the other side.

in this case, if the .999[r] ever stoped repeating, then it would not equal 1, but if it continues to reapeat then it equals 1.

 

[futuristicmonkey]

Originally posted by: Cogman
I had a math teacher explain it something like this. If you take a basket ball court, and travel half way, then travel half that distance, And so on, that is you do that for an infinit amount of time, you would reach the other side. But if you ever stopped traveling you would never make it to the other side.q]

Well, your math teacher was wrong. think about it - everytime you move, you move only half the distance. If evrytime you move half the distance, you will never completely get there. Think about half-life (not the game). So, if half of all the carbon-12 in an object decays ever 4500 years (nearly, i forgot the real amount) you will go: 1...1/2...1/4...1/8...1/16...1/32...and so on. It would never fully break down until it gets down to one atom...whatever. Anyways, because it gets so small, we usually say its all gone by the 10th time (unless youre doing something important.

I don't care how many 9's there are - .999999999999[r] doesn't equal 1. every nine you add on will only make it closer, but it'll never be 1.

 

[Cogman]

lol, and you missed my point compleatly. you think about it, every 9 gets it closer to one, correct? Well if their is an infinit number of 9s then the distance is infinitly small, something that is infinitly small is equal to zero. Try it out, 1/infinity.

You seam to have a incorrect preception of infinity, you seam to think that there is an end to the .99[r], but in fact, there is not. And as you have stated as you add the next nine it gets closer, never ending 9's means it is always getting closer.

Futuristicmonkey what math have you had?

 

[blahblah99]

Futuristicmonkey, you spout out a lot of crap but offer no proof except your own opinionated one. Show us a mathematical proof instead of "I don't care how many 9's there are, 0.9999.. will never equal 1".

Just because you can represent a number two different ways doesn't mean they're not equal.

0.125 = 1/8 = 2/16 = 4/32 = 8/64 and so forth. Jeez, some people just don't get it.

 

[Cogman]

yes I agree with blahblah99, futuristicmonkey prove it using math. We did our part in proving ourselves correct using math. Now you prove us incorrect using math.

 

[futuristicmonkey]

My math probably isn't as strong as the ret of you guys, but that has to do with my age. So, i go back to logic.

Of course 0.125 = 1/8 - youre just using a different method of displaying the number. Thats like saying 1/10 = .1 . But you guys are using the same format, twice, to represent one number - which doesn't make sense. And, maybe this is like that thing about the guy and the dog that was posted a while ago in this thread. It makes sense when u think about it, but when u use math, it screws it up. Whatever. I still stand by if it was equal to one, it would be written as one, not like 0.999999999999[r].

This is my last post on the subject.

 

[NichowA]

1. you can't add another 9 to it to make it "closer" to 1, by definition there is no end to the number of 9's on the end so how can you add one?
2. It is written as 1. It's just interesting that you can also write it as .999[r]. There are plenty of other interesting ways to write 1.

I'm guessing that you haven't taken integral calculus. When you do, ask your teacher questions about things like this and feel free to challenge him/her about them. That's how you learn. But one of the things you will learn is that when you take the integral of some equations across their entire domain (i.e.for every number that could possibly be used in the equation to produce a real answer), you can determine that there is a finite amount of area between the curve and the x-axis, while the curve itself is infinitely long. If you were to then rotate this curve about the x-axis, it would have a finite volume while having an infinite surface area. That is, you could fill it with a specific amount of paint, but you could never cover it in paint. There are other similar designs that have infinite perimeter and definite area (draw an equilateral triangle, then add an equalateral triangle that is half as big to each side, then repeat this process indefinitely) and other seemingly contradicting properties. That's what makes them interesting and worth discussing. It isn't always necessary to comprehend it, just to respect that it exists. It's like negative numbers, we have no real-world concept of what a negative number is. Or like temperature--we define things in common life as hot or cold, as heating or cooling, but in science there is no "cold." Things only have certain amounts of heat, and they transfer that heat to other things, or have heat transferred to them. "cold" is never transferred, rather "heat" is lost.

Interesting things like these are what make science and mathematics so amazing. I hope that as you take more and more courses in these subjects, you grow to embrace these quirks instead of rejecting them.

 

[Cogman]

yes, I guess thats a good way of saying it. .99999[r] is a only known because it is a special case. I think I stand with everyone when I say, After having Calc or even some precalc (not so much) you begin to look at certain aspects of math in a diffrent light. Like the slop of a line, their was always this cutsy algerbra formula that would solve the slope for you, but then you learn derivitives, and It becomes so much easier to use them instead of the algerbra slop formula (using the quick method of course)

 

[Kyteland]

Unless you've read all 4733 posts in this thread, you're unqualified to post on the subject.

http://forums.anandtech.com/messageview.cfm?catid=38&threadid=954453&arctab=arc

But seriously, take a look at the first few pages of that thread. You're rehashing a lot of material that's already been covered.

 

[Cogman]

I think that most people are uninforumed on that post. One guy said that if you do 1-.99999[r] the leftover number was the diffrence. Well the problem is there is no left over, the answer would be .0[r] which means there would be a 1 at the end, but the zeros never end, and no end = no 1.

I say most are uninforumed because most voted that it was not == 1, and im pretty sure everyone that has taken calculus will agree that it is = 1.