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
)Its poor scientific literacy.
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2=1.999...infinity! What are your thoughts?
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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
)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.
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.
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.
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.
There are six!
0.AAArepeating, 0.BBBrepeating, 0.CCCrepeating, 0.DDDrepeating, 0.EEErepeating, and 0.FFFrepeating!
(Sorry, though this thread could use a little lightheartedness.)
There are six!
0.AAArepeating, 0.BBBrepeating, 0.CCCrepeating, 0.DDDrepeating, 0.EEErepeating, and 0.FFFrepeating!
(Sorry, though this thread could use a little lightheartedness.)
Hexadecimal FTW!
****
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.
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
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.
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.
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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.
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.