Quote: "I simply infer that the result can become infinitely small and ever closer to zero, but never actually reach zero."
Shelton, I have to agree with IanM there...
x can get extremely large, as you've said... and as it get's so much more massive, the polynomial becomes,
f(x) = 1/x
f(x) = 1/uncomprehensibly massive number
That uncomprehensible number has been given the name infinity...
infinity isn't a point, or a number, it just keeps going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going... Well, you get the point.
Shelton, let's take your quote and rip it apart shall we?
Quote: "when x is infinity it meets that asymtotic point."
I say that infinity isn't a number, nor a point in time/space/anything. It is just a name we gave to identify those excedingly massive numbers that just get too freaking huge for our brains to comprehend.
Now, let's take your theory of it...
You say that it is a point ( not a number though )... It is a point somewhere, be it in space, in time, or on a number line.
And as you said, at infinity, the polynomial finally reaches that asymtopte.
This is not possible, as the polynomial never actually get's there...
*If* it was possible, you could plot that polynomiial on a number plain ( without a limited Domain or Range ), and look at it... It gets so very, very close to that asymtopte, but never, ever reaches it.
At this infinity point, you say that it is undefined, and is therefore 0 ( as 0 is undefined ), but that relation is not sustainable, because there is NO relation between infinity and 0.
Maybe in extremely high level math, infinity may be taken as 0 to help with an equation... But that's just for convenience, and when someone says "but that can't work" they have the discussion we're having now.
This just show's how we humans invented Math... the world would keep turning if 2 = 1, if Pi = 9.54, or if the diameter of the sun was only 3cm... Everything is relative, and to us, our "Math" system ( particularily the parts we're talking about here ) was made up so that we could have something semi-tangable ( I say semi-tangable, cos you can't actually touch math, lol ) for our minds to play with, and "understand"...
It's quite easy to say that the "laws" ( again, things that we made up ) of the universe must hold true... But, due to our math, we don't allow anything but the laws to hold true ( this is how we based the systems ), and thus, we cannot prove that these laws are false without first redefining our math system.
Ok, I don't know how much I repeated myself there, o rhow much sense that made, but that's my views... Oh, and it's kinda early here too, so my brains not functioning on the top level.
Jess.
[EDIT]
About that dumb thing trying to prove 2 = 1, you can't just go from;
(2 - 3)^2 = (4 - 3)^2
to;
2 - 3 = 4 - 3
You must evaluate what's inside the braces first...
ie,
(2 - 3)^2 = (4 - 3)^2
-1^2 = 1^2
thus,
Sqrt((-1)^2) = Sqrt(1^2)
Then, again, you MUST evaluate what's inside the braces,
Sqrt(1) = Sqrt(1)
therefore,
+/- 1 = +/- 1
Team EOD :: Programmer/Logical Engineer/All-Round Nice Guy