Name: Thomas

Question:
How is 0/0 ever defined.

Questions concerning division by zero, and in particular zero divided by zero, are not easy to answer. If you go to the first page of Math Central and search for 0/0 in the Quandaries and Queries section you will see some answers we have given in the past.

The essential feature of our answers is that if you attempt to use the usual meaning of division to define a/0, the resulting "object" is not a real number. If a is not zero then we sometimes call a/0 infinity, or minus infinity, depending on the sign of a. If a is zero then the resulting "object" is more complicated. Newton and Leibniz invented calculus to answer your question.