a maths problem

Right. You can't divide by zero right? That's undefined. There's no answer to the question, "what is some number divided by 0?", because unless the number is 0 itself, you can't get to any other number by multiplying by 0; and if the number is 0, then any number will work, so still no answer.

Consider an equation like y = 4x + 2. That's fine isn't it? There's no divide by 0 in there, nothing undefined.
If we differentiate this, to find the gradient at any point, we get dy/dx = 4. Why? Because simple differentiation means knocking the power of x down by 1, and multiplying by that power.
btw, if you don't know your differentiation, and are wondering what happens to the 2, well 2 is 2x^0, so it becomes 0*2x^(-1) - and no matter how difficult that exponent is, the 0 it is multiplied by ensures we can just forget about it.
so 4x^1 becomes 4*1x0, and as we know, x^0 = 1, all the time, no matter what x is, because x^0 means x/x = 1.

Except when x is 0, right? Because when x = 0, 0^0 is still undefined, because 0/0 is not 1, it is undefined.

A graph of y = 4 should be a straight flat horizontal line, cutting the y axis at 4. And it is, but if y = 4 is the same as y = 4x^0, then SURELY at the exact moment when x = 0 this graph will become instantaneously discontinuous?

In other words, for any value of x, y = 4; but when x = 0, the power of that 0 leaps into an equation it doesn't have anything else to do with and smashes it to pieces.

Can this possibly be correct? Any thoughts, jot them b'low.
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