<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>If you can, I'd like you to take your assertion of fractions equaling 1 and show as much with your process above and then show the equation that proves that (the theorem can be involved). I mean you wrote in your post that fractions added together will equal one (and then retort with confusion when i write ...division (fractions my man) added together...). Look at Feynman again oh great one. Not out of context at all. Ironically he was addressing this very thing. As for the angry assertions? just show your proof, don't say you have 'done it many times', and that is the resolution to your factotum argument. Now go brush up with your general relativity. I mean, your the master here as confidence is asserting here, so you should know that no straight line in the universe exists. SO when we deal with lines, we are dealing with truly mathematical concepts. The 'line' of our rulers are a best guess ( a very precise one, but without any standard, any true model, a line is an abstract concept). So again you should be able to prove how fractals equal a whole (you can use that elementary calculus). just prove it with a mathematical theory please. using elementary calculus I can prove how fractals will not. And thus why Pi is a fractal by purest definition. Through theorem and formula it is proven. I mean scientists didn't just give up and say, you know forget it, we don't think Pi has an ending, we'll just call it infinite. <br />Posted by nova_explored</DIV></p><p> If fyou understand calculus then you should already have seen this. </p><p>X + X^2 +X^3 + ... + X^n = [ X - X^(n+1)]/[1 - X]</p><p>You ought to be able to prove this for yourself. There are couple of ways to do it. One, often seen in high school is to proceed by induction on n. There is an easier way if you can find it. </p><p>Take the limit as n increases without bound to conclude that for X<1,</p><p>X + X^2 + X^3 + ... = X/(1 - X) </p><p>Substitute X = 1/2 to find that 1/2 + 1/4 + 1/8 + ... = 1</p><p>Your statement regarding general relativity and lines is roughly correct, in general relativity one deals with geodesics in a curved space-time. So what ? Of course lines are an abstract concept. So are geodesics. So is a manifold and hence so is space-time. </p><p>You statement regarding fractals is nonsense. Utter gibberish. Your statement that "fractals equals a whole" is completely meaningless. A fractal is a topological spece that happens to have a fractional (non-integer) topological dimension. Just to explain what that means is WAY beyond calculus.<br /></p> <div class="Discussion_UserSignature"> </div>