7 replies to this topic

[Infernity]

Not exactly physics but mathematics.

Where the hell am I wrong?



k=0.9999999999' ... /*10
10k=9.999999999' ... /-k
9k=9 /:9
k=1


Conclusion:

1=0.9999999999' ...



I went through this like 20 times, trying to find how come, [help] ...

[mellow]


-Infernity

[knite]

dumb

Edited by knite, 19 June 2006 - 07:19 PM.

[Normal Dan]

Where the hell am I wrong?

You've done nothing wrong. The conclusion you have come to is completely correct.

Mathematically 1 is equivalent to 0.999999999'

Infinity and limits are fun things to play with in mathematics. As you add more 9's to 0.999 it approaches 1. Once you have an infinite number of 9's, the number actually becomes 1. The problem you might be having is you're thinking of infinity as just another number, when in fact, it isn't considered a number at all. Infinity can do some unexpected things when you're not careful, like when you start using an infinite number of 9's.

Ask any math professor, and they will tell you, you've done nothing wrong in your math. If they do, then don't take any classes from them, and look at them funny when you pass them in the hall.

[chubtoad]

Yes 1=.999... One way to look at it is to just represent .999... as its corresponding infinite series, 9/10 + 9/100 + ... = 9(1/10 + 1/100 + ...).
This is 9 times the geometric series 1/10 + 1/10^2 + 1/10^3 which is (1/10)/(1-(1/10)) = 1/9. So we have 9(1/9) = 1.
Clearly all real numbers ( 4, 1/3, pi, e etc.)can be represented as an infinite series (first digit times 1/10 second times 1/100 and so on) in fact this is precisely the way one normally constructs the reals from the rational numbers! So as I think normaldan was suggesting the lack of intuition for real numbers is really a lack of intuition for infinite series. In particular the fact that an infinite series can sum to a finite number.

[Infernity]

[huh] Cool!! =]

knite, no I did minus the K in both of the sides...
You did 10k-k=9 indited of 10k-k=9k


humph, math is weird..

So I guess no one can explain exactly this thing can one?



-Infernity

[Brainbox]

In this area of mathematics, you also should be aware of the culprits our tools introduce.

Do the following on your calculator:

10 / 9 = 1.1111111…
Multiply by 9 and you get the original 10 back. At least with modern calculators.

However, if you enter 1.111111 with the maximum nr of digits, multiply by 9, it will not compute to 10, which is evident.

Basically, a normal calculator cannot deal with an infinite number of digits. However, it has some tricks inside so that it seems it can in certain situations like the example above. So, be very carefull to put results in the right context.

[Infernity]

I always use the "ans" button, obviously won't fill in the number written there, unless it is physics when we don't calculate exactly, we estimate gravity for example to 10, and not 9.8 ... he wants to see we know how to do the exercise, not how to calculate, so we just estimate the results so they will be like 2 or 3 numbers after the dot, doesn't really matter there.



-Infernity

[knite]

i remember once a series of arithmatic you can do on a certain number that SHOULD lead you back to the number you had originally, but for some reason does not. I cannot remember the trick though. Basically, there is no such thing as a completely consistent logical system, including arithmatic.