ok, here's something I've been buzzing at people for a few years (math people laugh and run from me)
0.999... (where the 9's go on to infinity) is equal to 1.
here's how:
One divided by three equals 0.333(to infinity)
(1/3) = 0.333...
Three divided by one equals three
(3/1) = 3
Also, since fractions are multiplied numerator*numerator and denominator*denominator:
(1/3)*(3/1) = (3/3) = 1
Keep in mind that 3*3 = 9, so it follows that:
(1/3)*3 = (0.333...)*3 = (0.999...)
We've used the same equation to achieve two distinct answers (3 and 3/1 are equal, remember!). Simple Junior High math allows use to substitute and eliminate common factors, so we are left with:
0.999... = 1
If you have a way of resolving this paradox, please post!
Cheers,
Iron Duke
0.999... (where the 9's go on to infinity) is equal to 1.
here's how:
One divided by three equals 0.333(to infinity)
(1/3) = 0.333...
Three divided by one equals three
(3/1) = 3
Also, since fractions are multiplied numerator*numerator and denominator*denominator:
(1/3)*(3/1) = (3/3) = 1
Keep in mind that 3*3 = 9, so it follows that:
(1/3)*3 = (0.333...)*3 = (0.999...)
We've used the same equation to achieve two distinct answers (3 and 3/1 are equal, remember!). Simple Junior High math allows use to substitute and eliminate common factors, so we are left with:
0.999... = 1
If you have a way of resolving this paradox, please post!
Cheers,
Iron Duke