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Author  Topic: A question of numbers (one for the maths fans)  
kuresu Member (Idle past 801 days) Posts: 2544 From: boulder, colorado Joined: 
actually, Mod's equation makes perfect sense.
This is going to asssume you have no basic algebra skills, just for simplicity.
What you do on one side of the equation, you must do to the other side of the equation. We establish that the variable, x, is equal to .999 . . . On the other side of the equation, then, 9x = 9. Now then, all that's left to do is find out what x is. x = 9/9, or x = 1. So, 1 = .999 . . .


riVeRraT Member (Idle past 207 days) Posts: 5746 From: NY USA Joined: 
Looking at the graph at the bottom of the first link, is always how I had pictured .999... in my mind. That is how I can conceive .999... becoming 1. The resolution of the infinite 9's becomes so small that it becomes 1.
My question is, why does .999... become 1, and .333... never be anything more that .333... ? Or how about this. In the equation 2+11=2 You can reverse the last 2 calculations, and still get the same answer ∞ + 1  ∞ = 0 ∞  ∞ + 1 = 1


riVeRraT Member (Idle past 207 days) Posts: 5746 From: NY USA Joined: 
Yes, I took algebra, but rarely have to use it. So it is very rusty.
That's about as far as I got, as I had a rough childhood, and had to drop out and start working. So I do appreciate everything, that everyone is saying to me here. It's not like I don't think about mathematical concept's all the time. It is my favorite subject. I use math immensely in my work, and my hobbies, but not at calculus levels. I have been thinking lately of going to college, to get an engineering degree, it's never too late. I invented parts of trigonometry out of necessity, because I am a master sheet metal layout mechanic. At one time, I needed to figure out what the other sides, and angles of a triangle would be, if I only knew one angle, and one length. I had invented some formulas, but I can't seem to find them. I later learned that it was similar to sin, and cos. Sheet metal fabrication is all about triangulation, and after doing for so many years, you gain a different perspective on the world. There is nothing I couldn't break down into a 2D pattern. I could cover you in metal. Now, about the formula. If that formula works for 10x, shouldn't it work for 2x? also shouldn't the result be similar when we use .333...? Why does .999... resolve to a 1, and .333... never resolve?


kuresu Member (Idle past 801 days) Posts: 2544 From: boulder, colorado Joined: 
I do believe that that should equal 1, not zero, but you might be right because adding one to infinity would give you infinity. Well, let's take a look at your .333 . . . problem. x = .333 . . . wheras in the other equation, 1 = .999 . . . All a man's knowledge comes from his experiences


kuresu Member (Idle past 801 days) Posts: 2544 From: boulder, colorado Joined: 
10x is just easier to use. But I'll go ahead with 2x.
x = .999 . . . x = .333 . . . .333 . . .does resolve, as a fraction. if you're looking to get it to resolve as a decimal, it will keep going for infinity. All a man's knowledge comes from his experiences


riVeRraT Member (Idle past 207 days) Posts: 5746 From: NY USA Joined: 
In wikipedia, what I am saying is considered wrong, but worthy of mention. quote: http://en.wikipedia.org/wiki/Recurring_decimal If we can't add a 0 to the end, then 2*.999... = 1.999... ? Even though 2*.999 = 1.998 Shouldn't infinity and time be directly related to one another? I was thinking this all along, but hesitant to say this.


riVeRraT Member (Idle past 207 days) Posts: 5746 From: NY USA Joined: 
2x=2? That assumes .999... is 1. That is wrong anyway. I think it should look like this: x = .999... Again, we are ignoring the last number, because there is no last number. That is what I find to be the problem.


kuresu Member (Idle past 801 days) Posts: 2544 From: boulder, colorado Joined: 
THe original equation, where you multiply by 10 proves that .999 . . . is 1.
.999 . . . * 2 does not equal 1.999 . . .. It would make less sense if this were so. Now, .999 * 2 is 1.998, because you are dealing with a nonrecurring decimal.
and you still end up with 1 = .999 . . . in that equation. All a man's knowledge comes from his experiences


lfen Member (Idle past 2965 days) Posts: 2189 From: Oregon Joined: 
It sounds like you are confusing concept with the universe. Infinity is a mathematical concept, just as a point and a line are concepts. A line is defined as having two dimensions. It has no width. You won't find actual lines out in the world that have no width. They don't exist. As far as I know at this point, well, at least for the known universe matter is assummed to be finite. There is a very large number of electrons but not an infinite number. But we are talking about mathematics. Do you accept that between 0 and 100 there are an infinite number of numbers (you can call them points as well) and that between .99999 and 1 there are also and infinite number of numbers? Infinite is not a number it means that no matter how far you count, or how many times you divide the line you can still keep counting, still keep dividing, there is no end to it. Now in the universe there may be a limit to how small you can make a division but we are talking mathematics here, pure concept. lfen ABE: I'm sure they prove infinity in number theory every day. Some one here can do this better than I but the proof is along the lines of pick some number as large as you want, call it n. You claim there is no larger number. But by adding 1 to it we have n+1>1. If you say that is the largest well we make another number by adding 1 to that. Edited by lfen, : after thought added


nwr Member Posts: 5586 From: Geneva, Illinois Joined: 
Neither of those actually make much sense. You cannot treat infinity as if it were an ordinary number.


riVeRraT Member (Idle past 207 days) Posts: 5746 From: NY USA Joined: 
Ok, try it with .5x
x=3 That works. x=.999... x=.333... x=? Isn't this proof you can't ignore the last number? Shouldn't the 10x in mod's equation be Edited by riVeRraT, : mistake


riVeRraT Member (Idle past 207 days) Posts: 5746 From: NY USA Joined: 
Concepts exist in time.
I do not accept it, or not accept it. I think about the possibilities.
A concept that has no end. So if the last number of a infinite numver has to change, then we have a problem houston.


riVeRraT Member (Idle past 207 days) Posts: 5746 From: NY USA Joined: 
Yes, I know, I was pointing out your mistake. 2*.999... = 1.999...8 Just like 10*.999... = 9.999...0 This is opposite of what I am trying to point out. But considered the correct way.


lfen Member (Idle past 2965 days) Posts: 2189 From: Oregon Joined: 
Two errors here. First there is no such thing as an infinite number. There are infinite sets, infinite series, etc. But infinity is not a number. Two the last number of an infinite number doesn't make sense. If you are referring to the last digit of a decimal representation of pi for example there is no last digit. There is not a last digit to .999... If there were a last digit it wouldn't be an infinitely repeating decimal, it wouldn't be an infinite series, it would be finite, that is to say countable. So there is no last digit, so the last digit, which never existed in the first place, can't change. There is no problem. The calculus works. You can cross a room. lfen


NosyNed Member Posts: 8863 From: Canada Joined: Member Rating: 4.6 
They both resolve. .9 is not equal to 1. .9... (the ... means an endless row of 9's. We need to be VERY careful with our notation) IS equal to 1 the difference is now zero. .3 is not equal to 1/3 .3... is equal to 1/3 You may think there is a diffence because the first case is a whole number (1) and the second is a fraction (1/3). That doesn't make a difference to what we are talking about.



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