Thread: Infinity

and if you take the derivative of infinity you get zero so that was point less

Infinity is not a number, it's not constant, and you cannot take it's derivative. You can take the derivative of a function which is unbounded. It could be 0, like the case of f(x) = ln(x), or it could be infinity still, like in the case of g(x) = x^2.

well actually infinity's derivitive is zero what is y= infinity it is a line and the derivitive of a line is 0

define infinity, mathematically.

well ok

limit of 1/x as x approches 0


or


x = x+1

If x = x + 1, then 0 = 1. Then you have a trivial ring, i.e. only one element, at best. The integers are an integral domain, which implies they are a ring.

Taking the derivative of your other idea would be:
lim h->0 lim x->0 ( (1/(x+h)) - (1/x) ) / h. That would reduce to (h*h)/(x*x + x*h). Since h and x are completely not related at all, we don't know which one converges towards zero faster. The derivative will actually change depending on which one does. In the case of 1/x, the derivative is -1/(x*x), so lim x->0 means the derivative will diverge towards minus infinity. You would need to pick a sequence that approaches zero, too.

The actual definition in terms of a sequence, is that
If for all a in the real numbers, if there exists a k such that the sequence x_n > a for all n > k, then that sequence diverges to infinity.