Suppose there is some unknown function, and you have to guess the equation for it. You can ask for a certain number of points of the function and then figure out what the entire thing looks like. How many points of it would you need to make sure you can induce its equation? It's seems like you would need an infinite amount, but even then, it could be a sin wave and you could be given just the maximum values of the wave crests (making it look like a straight line) or just any points (making it look like a long polynomial). Does this mean functions are characterized more than an infinite number of points?

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