My answer to my father about dividing by 0.

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Divide by zero and the answer is both plus infinity and minus infinity as a graph of 1 / x when plotted closer and closer to zero gets towards plus and minus infinity.

By the way I like cubedemon6073's avatar, it looks like a unit cell of CaF2 or UO2 (uranium dioxide's unit cell has the same shape as calcium flouride)

There are a few reason why it's not given a value.

In respect to the cartesian coordinate system, which is a simple x y coordinate system...example: go x steps over and y steps up

y expresses a distance from the origin along the y axis.

If we had some curve y = 20/x and we said that undefined is going to mean 10, we'd end up with 20/0=10

Meaning if we were at 0 on the x axis our curve would be 10 units up on the y axis. But that's not true because there is already a value, that if you divide 20 by, you will get 10. That value is 2. 20/2 = 10

So in that sense we cannot arbitrarily assign an actual value to undefined. They're all taken.

In practical applications, undefined takes the form of a concept.

What if, for example, I had some strange guitar amplifier which had a gain that could be modeled as

A = 10/R where R was some resistor (this actually is not how guitar amplifiers are really modeled but it explains my point)

What if I wanted to know what happens when I make the resistance of that resistor smaller and smaller and smaller.

On my graphing calculator, I can see my gain, A, will get bigger and bigger and bigger.
I can't actually really get to R=0 because I'm using wires and all wires have some resistance, but I can see that as my resistance R approaches 0, my gain theoretically approaches infinity.

In the real world, even if an amplifier could be described by that model, other things would eventually come into play to prevent the gain from actually becoming infinite, like the fact that we can't have 0 resistance with wires, or other physical characteristics would cause the model to break down, but in other areas, such as astrophysics, a similar model might be applicable for very large values before the model breaks down.

So in understanding the nature of things, we really use the equations in a qualitative way to get a feel for how things act.














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When you take the limit, yes depending on when whether zero is approached from the left hand side or the right hand side. What didn't mention though is that when you divide zero by itself, that can be made to approach any number you wish, depending on whatever the function is that you're taking the limit of. So 0/0 is completely indeterminate.

Lim (x ->0) 1/x does not exist.

ruveyn

I've always defined n/0 as infinity.

Infinity in the context of the real or complex number system is NOT a number.

It does not have the algebraic properties of a number.

ruveyn