Alright, I remember seeing this on the board in elementary school and being puzzled, but I dont recall the explanation. I was just reminded of it because I am writing a research paper in the library and the wall is littered with pseudo-intellectual graffiti and this problem: x= .99999 (repeating) 10x=9.99999 (repeating) 10x-x= 9.99999(repeating)-.99999(repeating) 9x=9 x=1 .99999(repeating) = 1 ?
In 9x=9 they have rounded to get to 9. It's the old problem that discounts the premise of numbers being real. If numbers are infinite, then how do you get from 0 to 1? 0.99999999999999999999999999999999999999999999999999999999999999999
The explanation is that there is no number between 0.99999... and 1. Let's look at it a different way. Suppose that 1 does not equal 0.99999... . Since they're not equal then one number is bigger than the other. Certainly you would say that 1 is larger than 0.99999... . That means there must be another number (or numbers) between 0.99999... and 1 on the number line. Which number is between 0.99999... and 1? Well, the average would be between the numbers. The average would be larger than 0.99999... and smaller than 1. What is that number? Well, to start the first digit must be 0 otherwise it would not be less than 1. The next digit must be a 9 otherwise it wouldn't be larger than 0.99999... . The next digit would also have to be a 9. Continuing along like this brings us to 0.99999... . But that is not larger than 0.99999... . Therefore, there is no number between 0.99999... and 1, and thus, they are equal. Another way to look at it is 1/3 = 0.33333... and 2/3 = 0.66666... . If we add those two together we get 1 = 0.99999... .
different topic, but in the philosphy building i remember seeing someones formula and from money = the root of all evil he calculated that women are evil. it was pretty clever but i cant remember exactly how he got there. i think the next step was money = women + power...dang, wished i would have written it down
The way the problem is written, you'll get 0.9999 (repeating) = 1, simply because of the infinite number of 9s after the decimal. Look at it this way. x = 0.999 10x = 9.99 10x - x = 9.99 - 0.999 9x = 8.991 x = 0.999 So in your problem, 10x will have 9.99 (repeating - one 9 at the end), instead of 9.99 (repeating). That's how you get x = 0.999 (repeating) instead of 1.
For a guy to satisfy a woman, he needs to give her time and money WOMAN = TIME x MONEY As we all know Time is money, so; TIME = MONEY Therefore; WOMAN = MONEY x MONEY And assuming money IS the root of all evil, WOMAN = Rt EVIL x Rt EVIL = EVIL
I think the age old question is.....are numbers infinite or finite between one and zero? No one can prove this.
I think the way the above problem is set up, it ignores the last significant digit (very similiar to Got em's response, though probably even more confusing). The correct way to approach the problem in my mind is: x= .99999 (repeating) = 1 - 1e-infinity 10x=9.99999 (repeating) = 10 - 10 e-infinity = 10 - 1e-(infinity - 1) 10x-x= 9.99999(repeating)-.99999(repeating) = (10 - 10 e-infinity) - (9 - 9e-infinity) = 1 - (1e-(infinity - 1) - 9 e -infitiy) = 1 - 1e-infinity x= 1-1e-infinity or 0.99999 continuos