by lukekh » Thu Feb 19, 2015 1:36 am
So if anyone actually wants to know why this is not okay, it's because the child is using the "Algebraic Limit Theorem" without first showing that the series dog+dog+dog+... converges. This means that we cannot treat the limit (as n goes to infinity of the sum of n dogs - the usual definition of an infinite sum) as real number (of dogs) and hence subtraction and addition are not defined well.
Sorry, I just needed to get that off my chest.
So if anyone actually wants to know why this is not okay, it's because the child is using the "Algebraic Limit Theorem" without first showing that the series dog+dog+dog+... converges. This means that we cannot treat the limit (as n goes to infinity of the sum of n dogs - the usual definition of an infinite sum) as real number (of dogs) and hence subtraction and addition are not defined well.
Sorry, I just needed to get that off my chest.