Quote:
Originally Posted by Squeek
Ok, so it goes on forever. That only means that the ratio of sticks to pebble increases as it goes on forever.
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I first want to point out that the ratio is always the same.
Next, I'd like to show one reason for infinity. Power series. Way back before you were born, calculators weren't invented yet. Someone had to program those calculators to approximate sine, cosine, e, pi, etc.
Power series approximate functions for a certain piece of a function. For example, we can approximate sine by (1/n!)·ƒ(n)(x0)(x - x0)^n. since n can be any number from zero to infinity, we can always achieve greater precision by making n larger. If infinity didn't exist (somehow) and say, this only worked until n=10, we wouldn't (Of course) be able to get any more precise after n=10.
Now, as technology keeps becoming more precise, more options are opening up. We can explore space, oceans, and other dangerous places.
These places are, well, dangerous. If you think about it, a loss of precision of .1 is not as small as it seems... It can cause a ship to not be able to have enough force to lift off, for just one example.