Can somebody who knows what they're talking about confirm this?

If I'm understanding this right, if I can find a complete set of 
orthogonal functions, I should be able to construct any possible 
function as a linear combination of them.

For example, the Fourier transform allows you to construct any function 
from sine and cosine functions. (On the other hand, except in the 
discrete case, you might need an infinite set of these functions to make 
an exact reconstruction... but the discrete case is the one that really 
interests me.)

If I'm not mistaken, "orthogonal" means that one function can't be 
constructed from the others (so there's no duplication of 
"information"), and "complete" just means you've got all the functions 
you need.

So, like, how do you tell if two functions are orthogonal? And how do 
you tell when a set of them is complete?

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