Math Problem....

[cwn723]

Hey, would you guys agree that 0.9^--=1?

PS: the ^-- is suposed to be the bar over top of the nine.

[RoBot1ks]

If it was rounded up....
Otherwise, it is veeery close

[cwn723]

WRONG... It is the exact same number

[noah03ark]

well the bar over it means its repeating.....so not really one..just 0.9999999999999999999 and so on for a long time

so no i don't agree

i do agree that its incredably close, like really f**king close to 1
but not exact, not equal

what i dont get at all is you're asking what we thing and if we agree then tell us we're wrong...

[cwn723]

If it is not the same exact number, you must then agree that there are no numbers in between it an 1, so what is the number in between?

[noah03ark]

there is no number in between

next thing i suppose would be 1, but then again the 9's could go on forever

[cwn723]

Ok, here is another way of explaining it:

Say there is a frog on one side of the room, and he is trying to get to the other side.
On His first jump, he jumps 1/2 of the way, the second jump he goes 1/4 of the way, the third jump, he goes 1/8 of the way, 4th is 1/16 of the way, and so on. Will the frog ever make it to the other side of the room?

[seikene]

Yes, but he will take forever, basically he's gonna keep cutting in half till he makes it over there. And yes, the problem can't be exactly 1 unless you round it, since -- is the top bar which makes .9 repeat to .99999....., then it's that number, and very close to one like he said, but not 1. Now if you made that sqiggly equal sign, then it would be correct, but no:
 -
.9=1

[budgray19]

even still taht haves nothing to do with math lol

[seikene]

You mean the frog thing? In a way, not really, but the way he put it, it will reach to one side eventually, it will just take a real long time :P, but unlike this problem, the .9 will keep going with repeating 9 till no end, so unless you estimate, it's impossible for .9-- to equal 1.

[cwn723]

It has everything to do with math, and the answer to the frog question is yes, but only if he can jump an infinite amount of times in a finite amount of time.
here proves that 0.9999999........=1

 0.9999... =     Sum         9/10^n
                     (n=1 -> Infinity)

                    =  lim               sum      9/10^n
                     (m -> Infinity) (n=1 -> m)

                    =  lim           .9(1-10^-(m+1))/(1-1/10)
                     (m -> Infinity)

                    =  lim           .9(1-10^-(m+1))/(9/10)
                     (m -> Infinity)

                    = .9/(9/10)
                     
                    = 1

[ccccpie]

even still taht haves nothing to do with math lol

"The word "mathematics" (Greek: μαθηματικά or mathēmatiká) comes from the Greek μάθημα (máthēma), which means learning, study, science, and additionally came to have the narrower and more technical meaning "mathematical study", "

So Technically it is, But No, .999999... does not = 1, as numbers go on forever.

In you're frog example there is an end, that being the wall, so it isn't a very good example.

No, there isn't a number inbetween .9 (repeating), But if you give an exact number, say, .9, there is a half because it has an ending spot.

Math is my worst subject so bear with me :S

[cwn723]

ok, im getting tired of being the only one who says it is, check my math, it proves it

[ccccpie]

I don't understand... Simplify what you are trying to prove please.

[cwn723]

I am trying to prove that 0.99999999999999............= 1

here is something i drew on paint... formulas that is.

[ccccpie]

Not sure, I've said my opinion on it, but that opinion is based on eighth grade math, lol. Sorry I don't have more knowlledge on the subject.

[cwn723]

Ok, well if anyone asks you:

0.9999999999........ = 1

It equals exactly 1, no higher, no greater.

[Reaper]

It's a gray area in math, to do it backwards you could do this

9/9 = 1
8/9 = .888...
1/9 = .111...
THEREFORE
.888...+.111...=.999... = 9/9 = 1

[cwn723]

Lol, reaper agrees with me.. nuff said.

[cwn723]

NOOOOOOOO, i shouldnt have invited you PvP, lol. Here, listen to DR. Math


Well, the proof for this is:

x = .9 repeating

10x = 9.9 repeating

10x - x = 9.9 repeating - .9 repeating

9x = 9

x = 1

Therefore .9 repeating = x = 1.

I always assumed that a variable cannot stand for two numbers.



Now remembery, the Numbers NEVER lie

[Reaper]

0.9 repeat does not equal 1. It only equals 0.9 repeat. Check to see how many sig. figs. there are and apply it to the problem.

Ex. sig. figs=4
0.9999

ex. sig. figs=7
0.9999999

depends on what theories in math you are looking at, which is why I said it's a gray area

Nothing in this world is 100%
the best we can get is 99.9...% because in everything there is a .01...% error


heres a different proof

.999... = [9(1/10)] + [9(1/10)^2]  +  [9(1/10)^3] + [9(1/10)^4] + [9(1/10)^5] + ... also written as  [9(1/10)^n] with n= 1-->infinity
this equals [9(1/10)] / [1-(1/10)] = 1

[cwn723]

Me and Reaper have proven it with simple math and numbers, .99999999999999999......... =1

Now, to the frogs!!!!!! I say that they will reach the wall, providing they can jump an infinite amount of times in a finite amount of time.

Say that:
1st jump=1/2 way across
2nd jump=1/4 MORE across
3rd jump=1/8 MORE across

So it becomes evident, that following this pattern, the frog WILL make it. Discuss.

[ccccpie]

Me and Reaper have proven it with simple math and numbers, .99999999999999999......... =1

Now, to the frogs!!!!!! I say that they will reach the wall, providing they can jump an infinite amount of times in a finite amount of time.

Say that:
1st jump=1/2 way across
2nd jump=1/4 MORE across
3rd jump=1/8 MORE across

So it becomes evident, that following this pattern, the frog WILL make it. Discuss.

There's nothing to discuss. It will make it and that's that.

[cwn723]

OK fine, no discussion, LOCKED

Jk, i cant LOCK!

[ccccpie]

:/ The thread creator can lock there own, lol, but i'd keep it open for further discussion.

[Timmy]

Its already been said man, it depends on what you are applying the number to.

if you apply 0.9 recurring into an exponential you can see that the X values (this is a loose hypothetical situation, dont get pedantic and pick at my choice of variable) would get closer and closer to 1 but never reach it, it would just keep increasing in significant figures

your frog situation is a pile of steaming BS.

You have not made it evident at all, you have shown 3 fractions which show that it will make it 7/8 accross the room

if we went another step onto 16ths you would show that it will make it 15/16 accross the room

31/32
63/64
127/128
....

NONE of those fractions are equal to one, they will approach it for sure, but never reach it, and if you think 0.9 recurring and 1 are the same thing...you havn't shown it will reach 0.9 recurring either. So you havn't done ANYTHING at all, you were closer to disproving your situation then proving it for this area of mathematics/science

Your sum to infinite of a geometric series, is once again a poorly used example. 1) You supplied the formula, but no examples such as how PvP did, thus giving no evidence, or even introducing a question that relates to the theory 0.9 recurring = 1

lets use your frog situation again, the exact numbers and situation

a= T1 = 0.5
r=  T(n+1) / T(n) = 0.5

|r| < 1 therefore the series converges and has a finite limit. Using the formula:

S(infinite) = 0.5/0.5 = 1

thus proving........Absolutely nothing towards your statement, because it is the sum of numbers in the sequence (ie: A SERIES) approaching one, not 0.9 recurring. It merely proves that he will make it accross the room at a decreasing rate of speed as n approaches infinite. The formula clearly shows a 1 when you divide 0.5 into 0.5 NOT 0.9 recurring

Honestly man, the numbers may not lie, but when you dont use them correctly you can look like a real dousche

[*FuFa]

Reaper never said "Hey, you are god damn right, so 0.9999 infinite is 1.0" all he has proven is that it's a gray zone.

Now to the frog thing.

No, it will never reach the other end. Like Timmy said quote "It merely proves that he will make it accross the room at a decreasing rate of speed as n approaches infinite." meaning, the frog will need a infinite amounts of trys to get to the other side, thus never reaching it.

So I will simply say to both questions:
No.

0.9 infinite =/= 1
frog never reaches other side, because 0.9 infinite =/= 1

[noah03ark]

yeah the frog thing is weird. but if you exponetnailly cut the distance in half each time its never going to reach it because you cut it an infinite number of times to somthing so small...like really f**king small... that it will never reach it

i agree w/ fufa

0.9 repeating (infinitely) =/= 1

[dedafmonteur]

0,9999999 is not a whole pie
 
1 is a whole pie


see the difference?


over here they call it the black zone, you just cant say it's 1

[noah03ark]

0,9999999 is not a whole pie
 
1 is a whole pie


see the difference?


over here they call it the black zone, you just cant say it's 1

there are a few proofs i've seen, but this still falls in a very very grey zone thats up to questioning and interpretation

basically yeah

'cept the nines go on forever so its infinitely small