MWresearch Posted August 27, 2015 Share Posted August 27, 2015 (edited) Just what the title says. Say I have some random equation like 2^x, then I have some random equation that I tested and it gives me the points (1,2), (2,4), (3,8), (4,16), (5,32), (6,64), (7,128) but there's no proof it works for (8, 256) other than by testing it to see it works for x=8, if I assume the curve is continuous, is there any sort of weak proof that says it's the equation 2^x? Every taylor series should be unique, yet for any given equation that was derived purely from integers, I could use some kind of a*cos(bx)+c that generates a coefficient of "1" for any given integer. For instance, the equation y=2^x generates (1,2), (2,4), (3,8), (4,16), (5,32), (6,64), (7,128). However, the equation y=(2^x)*cos(2*pi*x) generates (1,2), (2,4), (3,8), (4,16), (5,32), (6,64), (7,128) as well, so how do I deal with this? So if I assume there's no trig involved, there's nothing else that could perfectly match another continuous operator at each regular interval but is completely inaccurate at interpolated x values right? Or no?? So is there some weak proof that works if I assume no trig functions are involved? Edited August 27, 2015 by MWresearch 1 Link to comment Share on other sites More sharing options...
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