(August 10, 2013 at 11:37 am)FifthElement Wrote: In algebra (where division is defined as opposite of multiplication) division with 0 is indeed undefined but the limit of 1/n as n approaches zero is infinity.
Weird, isn't it ?
that is because dividing anything with a decimal (which can be written as 1/x) is actually multiplying it with the denominator of that fraction (x). so 1/n as n approaches 0 gives you 1 divided by n=1/x where x is a very big number so that 1/x is almost 0. So you have 1/n divided by 1/x = 1 * x = x (approaches infinity).
It's like saying if a quarter of a person gets 1 apple, how many apples does a whole person get? so just 1 divided by 1/4, which is 1 x 4 = 4. So if 1/1000 of a person gets 1 apple, a whole person would get 1000 apples. The smaller the fraction the more apples the whole person gets. And the smaller the fraction the more it approaches 0.
Anyway, the sandwich analogy is great. I use it to explain chemistry a lot.
