Ok I realize the Pythagorean Theorem is correct. I completely get that very basic concept this is just a question I have. On a right triangle a^2 + b^2 = c^2 with c being the hypotenuse. But if instead of the hypotenuse connecting the two legs you had a jagged line that went halfway up then half way to the right and then the other half to the up and the other half to the right. That line would be equal to a + b because it is going the same x distance as a and the same y distance as b. Now if you continued to decrease the intervals at which you switch going up and then to the right: You would end up with a line similar to a ton of tiny stair steps connecting the legs a and b This "stair" line would also be equal to a + b Now finally if you made the intervals in which you take these steps infinitely small (Or take the limit as it approaches zero) the "stair" line would be approximately equal to the hypotenuse and thus c = a + b But that is completely contradictory to the Pythagorean Theorem. Now I know you can approximate any function (Including a hypotenuse) with tiny step intervals because of Plank's theories on Quantum mechanics and how digital signals can perfectly recreate analog signals (Digital signals are in step form) I fail to see where my flaw in logic is. I know I made a mistake somewhere but I cannot see it, much appreciation if someone could point it out.