Become a MacRumors Supporter for $50/year with no ads, ability to filter front page stories, and private forums.
Am I missing something here?

1.99999999999 with a finite number of 9's is not the same as 1.999...999 with an infinite number of 9's. (I've been beaten by ages by Eric5h5 though :eek:)

This thread really surprises me. I learned this stuff in 9th grade. It's stuck with me ever since. I went to a pretty good school, but surely you folks learned this kind of math at some point in high school? Or even college?

Its poor scientific literacy.
 
Its poor scientific literacy.
I think many people learn this kind of thing in school and then forget it -- unless it's related to their further studies or they find math to be fun and interesting on its own.

Speaking of fun, tell your friends that the average person has 1.9999... parents and see if they believe you.
 
0.(9) is another way to write "1." This is a very useful concept for dealing with curved lines.

You've got me interested. Please elaborate.

BTW, not to nitpick, but isn't "curved lines" sort of an oxymoron? Aren't they just called curves?
 
You've got me interested. Please elaborate.

BTW, not to nitpick, but isn't "curved lines" sort of an oxymoron? Aren't they just called curves?

Yes and no. In strict mathematical terminology, a 'curve' can include straight lines.

Anyway, if you are interested, you should consider taking some analytical geometry and calculus courses to learn the fundamentals. Of course, judging from some of the participants of this thread, this isn't a guarantee of understanding. Specifically, if you understand what a limit is and what it represents, then you will understand why 0.(9) = 1. (There is no last 9!)

As I mentioned, there are different ways of representing 1 depending on the type of mathematical problem with which you are concerned. If you're working with circles, your representation might include the term pi.
 
Yes and no. In strict mathematical terminology, a 'curve' can include straight lines.

That was sort of my point. A line is a straight curve. To say straight line is redundant and to say curved line is oxymoronic; in strict mathematical terminology as you say. But at any rate, that's not important.

As I mentioned, there are different ways of representing 1 depending on the type of mathematical problem with which you are concerned. If you're working with circles, your representation might include the term pi.

It sounds like you're referring to using a symbol, like "pi" or "e", to represent a number that is not possible to represent exactly with simple decimal notation. Were you talking about "pi" and circles when you said "This is a very useful concept for dealing with curved lines."? If so, there's no need to expound anymore. I was just curious if it was something else that I might not have heard of before.

I would probably make a distinction between a number like 1, pi, or e, and an expression like -cos(pi) that evaluates to 1. I personally would call [-(e^i(pi))] an expression rather than a number. Only because it involves operations like multiplication and exponentiation.

I'm a little torn though about whether or not I would call 0.(9) a number. I can see a case for it, but really, when I look at it, I see a representation of an infinite series that evaluates to 1. Thus in my mind, 0.(9) = 1, but I wouldn't necessarily say 0.(9) is 1. Probably a silly and possibly an incorrect distinction.
 
I'm having a great discussion with a friend about the following...

1. if x=1.999...infinity, then 10x=19.999...infinity. Subtracting 10x from x gives 9x=18. Dividing both sides results in x=2.

2. Using your calculators on this one. 1/9=0.111...?. 2/9=0.222....?. 3/9=0.333...?. 4,5,6,7,8 follow the same pattern. What, then is 9/9? It is 0.999...infinity.

Do you think those are valid? I think they are and thinking in infinite terms 1.999...infinity is equal to 2.

My friend thinks he can add any number to infinity because he just can.

Food for thought. Any you want to add?
****

You'll be unable to accomplish this via a computer.

There are a couple of acceptable proofs.

For the purpose of not being able to use a solid bar over a number, I will use an underscore after the digit. So for example, 1.999 (with the 9 repeating) would be written 1.9_

1.9_ = 1
let x = 1.9_
10x = 19.9_
10x - x = 19.9_ - 1.9_
10x - x = 18
9x = 18
x = 2


There's also another one

1/3 = 0.3_
2/3 = 0.6_
1/3 + 2/3 = 0.3_ + 0.6_
1 = 0.9_
 
2 = 1.999....

Is still an approximation.

Think of it this way:

If you wish to create a filter that will block particles of 2.0 diameter, holes of diameter 1.99999... will not block them reliably.
 
2 = 1.999....

Is still an approximation.

Think of it this way:

If you wish to create a filter that will block particles of 2.0 diameter, holes of diameter 1.99999... will not block them reliably.
No it's not. 1.9999... is 2. Period. 1.111111111111111... is 1 and 1/9. 1.9999999999... is 1 and 9/9 or 2
 
Nothing can move!

If an object moves from point A to point B, it must have been in motion for some length of time, starting at time S and ending at time T. But it can't actually move during that time period because at any given instant between S and T it is not moving. Why? Because an instant is an arbitrarily small lengthlof time during which we can take a snapshot and see that the rate of speed is zero.

Mathematically: We know that distance = speed x time. For any speed and positive number N that you specify, I can make sure the instant (time) is short enough so that distance will be less than N. Therefore, distance (which is a physical measurement so it must be non-negative) is smaller than any positive number. Hence distance is 0 at any instant.

No matter how many zeros you sum (even an infinite number of them) you still get zero. We know that the object is not moving at any given moment (instant). So across all moments from time S to time T, the object has not moved.

And with that I have proved why the cars on the 405 Freeway in Los Angeles never move!

The only thing you've proven is that you didn't listen in high school math, or you're deliberately trolling.

The distance is a function of time and the speed is defined, at any given point, by ∂d/∂t. Unless the car is actually at a full stop (say, at a red light - but why were you trying to find the speed of a stopped car anyway?), the speed is never zero.

Because an instant is an arbitrarily small lengthlof time during which we can take a snapshot and see that the rate of speed is zero

No. An "instant" is a very short, teeny tiny amount of time ∂t (which can never be zero) where the car manages to travel the distance ∂d. What you're doing is dividing by zero, which teachers hopefully should've taught you is a no-no even before you hit high school.
 
Last edited:
The only thing you've proven is that you didn't listen in high school math, or you're deliberately trolling.

The distance is a function of time and the speed is defined, at any given point, by ∂d/∂t. Unless the car is actually at a full stop (say, at a red light - but why were you trying to find the speed of a stopped car anyway?), the speed is never zero.
You nailed it. When you measure the difference in position as a function of time as time approaches zero, the difference doesn't magically become zero. The derivative indicates that the car is actually still moving.
 
The only thing you've proven is that you didn't listen in high school math, or you're deliberately trolling.

The distance is a function of time and the speed is defined, at any given point, by ∂d/∂t. Unless the car is actually at a full stop (say, at a red light - but why were you trying to find the speed of a stopped car anyway?), the speed is never zero.

You must have missed the memo, but Doctor Q is one of the aliases used by Zeno of Elea.
 
Because you said so, right?

If you have a hole of 1.999999999999999999 etc. diameter, something 2.0 in diameter will not fit in it.
Yes, it will.

If you have a hole of 1.999999999999999... ft diameter, you have a hole of 2 ft diameter. It will fit.

Stop trying to conceptualize it visually. .9 repeating is 9/9 or 1. Period.
 
Register on MacRumors! This sidebar will go away, and you'll see fewer ads.