The Calculus/Math Help Thread

der Astronom

der Astronom

Is a bigot for agreeing with Jim
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...Well, most of us. If you have any problems with math or calculus, I'll be willing to help you solve your problems. If anyone else would love to join in and help, please do so. I'd love it when a bunch of other people give alternate solutions to a problem.
 
Alright Angelus, I need your help with the following problem.

x = 0.999999999999999999 (this number goes is infinite)
10x = 9.9999999999999999 (the numbers behind the decimals are infinite, still)
9x = 10x - x
9x = 9.999 - 0.999
9x = 9
x = 9/9
x = 1

See the problem? We first let X = 0.99999, but then we can allow it to equal 1. How can this be so?

It works in the same way with any number such as this, as I've discovered. If you need me to explain the equation further, I'll do it. It's the current phase in my school :P
 
Well, I know that 0.999... is supposed to be 1, as I learned somewhere.

If you look at the third line, you will see that this doesn't work for a terminating decimal. This is because if you used 0.999, you would get 9.99-0.999, which doesn't give you x=1. But with 0.999... you will still get the same number, except the decimal place has moved...only it hasn't. That is, there is still the same number of 9's behind the decimal point. Since you had an infinite number of them to begin with, and moving the decimal place a finite number of times does not change infinity.

Interestingly enough, you can obtain the fractional form of any repeating decimal by dividing the number by 9. For example, 0.777... is 7/9, but as you can see, you don't get one for 0.999... because it's 9/9=1.
 
I think I follow that ...

The reason we all believe that it works, is because of the infinite numbers after the decimal point. They cancel each other out, so we are finally left with 9 - 0, which = 9. So, do get X on its own, we divide 9 by 9, giving us 1.

It also worked with 0.5999... but we haven't worked out any more numbers.
 
All right, I know this topic is a little old, but I love math (was a math major in college).

Anyway, .9 repeating is mathematically equivalent to 1 (the "best" way to prove it is with a geometric series). .99999... = 1 no ifs, ands, or buts about it. They are the same even though they look different.

In fact, you can write any repeating decimal in fractional form by dividing by so many 9's. So, .3 repeating = 3/9 = 1/3, .125 repeating = 125/999, and so .9 repeating = 9/9 = 1. And something like .2345666666... = 2345/10000 + 6/(9*10000) = 21111/90000 (also something that gets proven with geometric series).

And so .599999... = 5/10 + 9/90 = 6/10 = .6. In fact, any terminating decimal number can be written in two different ways.

Fun fun fun!

Oh and I'd also love to help out if anyone has any questions with math related stuff. I even worked as a math tutor for a couple years.
 
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