Weekly Top 200 - 7/25/2014

[TheGreatErenan]

0/0 is an indeterminate form.

x/0 where x != 0 is undefined because the result would logically be the number which when multiplied with 0 would yield x. There is, of course, no such number.

On the other hand, the result of 0/0 would be the number which when multiplied with 0 would yield 0, but this is true of every real number, and so it is indeterminate.

Note that even with limits, functions that approach 0/0 do not necessarily yield 0 when you take the limit. Consider the function x/x. If you take the limit as x approaches 0, the answer is 1. On the other hand the limit as x approaches 0 for x^2/x is 0.

Again, this is why it is an indeterminate form.