WHAT DO YOU GET WHEN YOU DIVIDE A FINITE NUMBER BY ZERO?
There are likely to be different responses to the question such as "it can't be done"or the answer is "indeterminate" or even "infinite".A good answer would be that from an applied maths point of view dividing by zero is a futile exercise.
WHY FUTILE?
As an example consider an equation of the type:
y=k/x (k could be a constant)
We could describe that as x gets smaller y gets bigger.It is a good description and one that can be used in both pure and applied maths.But at some point the two branches of maths will begin to differ.Pure(theoretical) mathematicians may consider that x can continue to get smaller,it can approach zero and even, perhaps, reach zero.
Applied mathematicians will know that there are limits to the smallness of x and that x cannot reach zero.Exactly what those limits are depend on the equation under consideration and it should be the job of an applied mathematician to try to gain a full awareness of the limitations of the equations used.
WHY FUTILE?
As an example consider an equation of the type:
y=k/x (k could be a constant)
We could describe that as x gets smaller y gets bigger.It is a good description and one that can be used in both pure and applied maths.But at some point the two branches of maths will begin to differ.Pure(theoretical) mathematicians may consider that x can continue to get smaller,it can approach zero and even, perhaps, reach zero.
Applied mathematicians will know that there are limits to the smallness of x and that x cannot reach zero.Exactly what those limits are depend on the equation under consideration and it should be the job of an applied mathematician to try to gain a full awareness of the limitations of the equations used.