Another question for the science type folk out there...
Why is a number divided by 0 said to be undefined? In my mind, it should be positive or negative infinity. Since infinity is not a real number (as proven by the notion that infinity is all and adding or subtracting any number from it will still yield infinity) it would not be subject to the standard rules of division wherein the process could be reversed by multiplication. I understand that division by definition must work where a/b=c only where c*b=a for any real number. However, zero is not a true quantity or number. It is a concept that allows us to deal with non-existence. As such, the definition of division does not hold constant since division can only be done using real numbers. With that being said, we can see what division by 0 ought to be by setting up some simple limit type equations. By taking the limit of any real number divided by a number approaching 0, the result will become increasingly large in either a positive or negative direction, approaching either positive or negative infinity. The only exception to this rule is in the case of 0/0, in which the entire set of real numbers would also satisfactorily work by the aforementioned definition of division. I guess, in short, that I'm confused as to why we can't deal with something that seems so easy to me when we are willing and able to use concepts such as 0, infinity, and imaginary numbers in mathematical equations all of the time. This has been bothering me ever since high school algebra and I was reminded of it today while reading a book and would like to see if anyone else has any ideas.
Josh
Josh