12/20/2007, 09:08 PM
Well, I'm sure everyone has his own way of thinking of infinities and infinitesimals that is unorthodox. Personally, I think of "Big Oh" limits of functions taken to infinity, but using only a power of x.
For example, let's say I have a function f(x), and I want to find a power of x that represents the big oh limit. Well, f(x)=x^2+x will have a power of 2. For f(x)=3x^2-x^1.999, it's still 2.
But what about f(x)=ln(x)*x^2?
It's big oh limit will be greater than 2, but smaller than all real numbers greater than 2. I consider this 2 plus an infinitesimal. YMMV.
For example, let's say I have a function f(x), and I want to find a power of x that represents the big oh limit. Well, f(x)=x^2+x will have a power of 2. For f(x)=3x^2-x^1.999, it's still 2.
But what about f(x)=ln(x)*x^2?
It's big oh limit will be greater than 2, but smaller than all real numbers greater than 2. I consider this 2 plus an infinitesimal. YMMV.
~ Jay Daniel Fox