anotherlife
Gold Member
Dividing by zero? It's common to multiply two sides of an equation by zero, but divide? Can't think of when that would be legitimate.Try not to get too technical, but can anyone explain this in common English?
I went home and thought about it last night, but for the life of me, I can't understand why if it applies to division, it doesn't apply to the rest. What is different about division that doesn't allow that?
We can do it by example, how about this, cut up a bread to infinitely thin slices. Then you will need to take away infinitely many slices to consume your original loaf of bread so the result of your division is negative infinity.
Now take many infinitely thin slices to make up your original loaf of bread. You wil need all the infinitely many slices to reconstruct your loaf of bread so your result is positive infinity.
But what if your slices are not infinitely thin but zero thin. Since 0+0=0, not even infinitely many slices will give you back your bread. This is why the division by zero is a special case, breaks every number even infinity itself.
So it is axiomatically defined as error. It's effect is to cause a discontinuity in everything it touches, a singularity if you like. The division by zero is frequently used in mathematics in many calculations for example the estimation of system stability in the general sense, where the locations of such divisions are called the poles of the system.
You can think of it as two polynomials, one dividing the other. The ratio of the two polynomials is the system output. The numerator polynomial is the forward behavior of the system, and the denomerator polynomial is the feedback behavior of the system, a memory, if you like. Each of the polynomials are linear combinations of the system input raised to various powers. This model describes every system in the universe generally. To calculate the physical poles of the system, you equate the enumerated result of the denominator polynomial to zero, i.e. you assume that you are inside a singularity of the system. You work backwards from this zero equation to find out what sort of system inputs could be capable to produce the singularity. So to answer your question in short, you don't do the division by zero but assume it then work backwards from that assumption to find the input values that can cause it.