For all you math-minded people out there...

[Balbus]

.999999999~ = 1

Yes or no?

[redqueen]

1. Um... yes?

With the the ~ there... I just couldn't answer otherwise.

[coloradodem2005]

2. Yes. It is.

[KitchenWitch]

3. Approximately, rounded to the nearest integer, yes.

[kick-ass-bob]

4. what do you mean by ~ ?

are you repeating the 9 or are you trying to say "approximately equal to"?

Or something else?

[kick-ass-bob]

7. actually, I will just say this:

Asymptotically .99(repeating)=1

[billyskank]

5. I'd say it depends on your perspective!

:P

[LiberallyInclined]

6. close enough for government work..

nt

[billyskank]

8. Hell, as far as electrical engineers are concerned

0.9 = 1 or may as well be!

[kick-ass-bob]

11. I thought that was

.5 = 1 for EE's!

:P

[Crazy Guggenheim]

13. Ever notice how there ia a EE in the middle of the word geek?

[kick-ass-bob]

14. LOL!

:7

[hunter]

18. Close enough is good enough.

Digital math on silicon. Yum.

Once I rose above the noise and confusion
Just to get a glimpse beyond this illusion
I was soaring ever higher
But I flew too high

Though my eyes could see I still was a blind man
Though my mind could think I still was a mad man
I hear the voices when I'm dreaming
I can hear them say

Carry on my wayward son
There'll be peace when you are done
Lay your weary head to rest
Don't you cry no more.

Kansas. It's a state of mind.

[valis]

9. NO, when you think about the lottery.

.99999999 is the chance you may have of NOT winning. There is a small chance. 1 means there is zero probability to win (e.g., if you don't buy a ticket).

[Crazy Guggenheim]

10. No. The way that is achieved is ...........

1/9 = .11111111111..... So 9 X .11111111111... = .9999999... = 1

Now this is the problem. People don't realize there is a remainder of .00000 .... 1 when dividing by 9. It can confuse a lot of people even Mathematicians.

[Balbus]

15. But there's this formula...

Let's say x = .999 ~
10x would = 9.999~
if you subrtact the value of x from both sides you'd have 9x = 9.0
Divide both sides by 9 and you end up with x = 1

[redqueen]

19. Sweet!

:loveya:

[Crazy Guggenheim]

20. Umm. No. It works out that you are mutiplying by ten then

subtracting the exact remainder from both sides.

[Balbus]

23. But isn't the remainder the value of X?

I don't think I understand what you said.

[kick-ass-bob]

22. I'm not 100% sure that equation is correct.

Because if you multiply by 10, you break the infinite nature of the number, leaving a ......9 on the very end.

Maybe.

[Crazy Guggenheim]

24. That;'s it..

[cosmicaug]

36. That's it???

That's it meaning that you agree that when you multiply by 10 you "break the infinite nature of the number"? What the grossly mutilated transexual spotted peccaries are you talking about?

[Crazy Guggenheim]

37. If you look at the Differential Operator it all makes sense.

:popcorn:

[cosmicaug]

39. You've got to be trolling!

Please tell me that you're trolling?

[kick-ass-bob]

41. decimal representations of fractions are not 100% accurate.

That is why they aren't mixed together in mathematical proofs.

[cosmicaug]

44. It depends on what you mean.

kick-ass-bob wrote:

decimal representations of fractions are not 100% accurate. That is why they aren't mixed together in mathematical proofs.

It depends on what you mean by that. Certainly there's the obvious counterintuitive thing about the notation for .9~ representing the same number as 1. That's just goofy but it doesn't make it less true.

[Crazy Guggenheim]

43. I've been exposed! I'm from the Eliptical Geometry Forum. I

should have known. We don't really hate you people, and don't hate me. It's just that ever since the so-called proof of the Four Color Conjuncture it's really infuriated the purists.

:cry: :pals:

[cosmicaug]

49. Masterful!

Crazy Guggenheim wrote:

I've been exposed! I'm from the Eliptical Geometry Forum. I should have known. We don't really hate you people, and don't hate me. It's just that ever since the so-called proof of the Four Color Conjuncture it's really infuriated the purists.

T'was masterful trolling, whoever you are and wherever you come from.

[Crazy Guggenheim]

50. Thank you! Thank you! T'would have not been exposed on

any other forum! Galios' memory is honored!

[kick-ass-bob]

38. wow, chief, chill.

There are 2 theories about it - it is not completely cut and dried.

[cosmicaug]

42. It's cut and dried, dude!

kick-ass-bob

There are 2 theories about it - it is not completely cut and dried.

Balbus presented a very simple mathematical proof that .9~ is just a different way of writting 1. Of course, it's cut and dried. That's what it means in mathematics when one presents a valid proof of something.

[Balbus]

25. Then if .999~ and 1 have different values.

What number comes between them?

[Crazy Guggenheim]

28. None because .9999~ is used to represent the cardinality

of the only number before 1.

On Edit:

Cardinality meaning the order of numbering. Ex., 1,2,3,4,.... Not, 1,8,3,0, ... is not ordered. So it's just how the values are ranked.

[kick-ass-bob]

30. what he said.

:P

[Balbus]

32. So .999~ is only a theory and not a real number?

And thanks for the edit - I was going to have to look up "cardinality: :P

[Telly Savalas]

34. You're making that up.

[cosmicaug]

35. Thank you.

Balbus wrote:

Let's say x = .999 ~
10x would = 9.999~
if you subrtact the value of x from both sides you'd have 9x = 9.0
Divide both sides by 9 and you end up with x = 1

Thanks. An actual valid mathematical proof and it's concise and easily understood to boot. I don't see why it's hard to get for some.

[cosmicaug]

12. Indeed it does.

Indeed .9999~ = 1

Cecil Adams covers this issue at http://www.straightdope.com/columns/030711.html

[Crazy Guggenheim]

17. I don't think so. See my great proof above. lol.

[cosmicaug]

33. Your proof?

Your proof is exactly the same one that Cecil shows (O.K. so he goes with thirds rather than ninths but it's still the same thing). How can it be proving the opposite?

[redqueen]

21. Thanks for that link...

makes it easy enough for anyone to follow. :)

[Rabrrrrrr]

16. No, not = but damned close to, mathematically speaking

If you were doing science, however, you could easily round it off to one, unless you were doing a calculation with an infinite number of significant digits. And since you would never be doing that, just call it 1 and be done with it.

[Crazy Guggenheim]

26. This is going to turn into a flame war!

:woohoo: :hide: :popcorn: :donut:

[zbdent]

27. If you're a first-issue Pentium chip

yes . . .

[Crazy Guggenheim]

29. No it's more like pi = e = 1/9

[Crazy Guggenheim]

31. Math Rules! Hey who says Math is cut and dry??

Heavy metal guitars come in!

[IrateCitizen]

40. Absolutely, in terms of "approximately equal to"...

Now, if you're dealing in absolutes, then it is clear that the two are NOT equivalent. However, they are approximately equal to one another.

[aeolian]

47. Only if the 0.999 number is not infinitely repeating

In the limit where 0.999... goes on forever, then the difference between 1 and 0.9999... goes to zero.

[aeolian]

45. Yes, by definition

If you mean the number 0.9999... repeating to infinity, then yes, it is exactly equal to 1.

Little trick o' the math. :)

[bleedingheart]

46. no but then again it could be seen that way if you study Limits

[aeolian]

48. It has to be seen that way if you study limits,

and the concept is used in lots of number theory proofs.

[Crazy Guggenheim]

51. Agreed in "the limit" it does approach 1. But that's just in

"the limit".

[Crazy Guggenheim]

52. Ok look at it this way. When you divide any number by any other

number this is what you are doing. Say 23 divided by 4. So, you have 5 with a remainder of 3. Now when you divide 1 by 9 you always have a remainder of 1. So the answer to 1/9 is not .11111111~ but rather .111111~ with a remainder of 1.

The Gods of Mathematics have rejoiced!

[Balbus]

53. Wouldn't that be a remainder of

.~0000001? But .~00000001 is not an actual number :shrug:

[Crazy Guggenheim]

54. No. Because you got that number from Xn not the Xn+1 iteration.

Think about whenever you do a division.

[Balbus]

55. It's impossible for .11111 ~ to have a remainder - it's infinite.

Just like 1/3 equals .333333~ without a remainder
And 2/3 equals .66666~ without a remainder.