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I was just thinking to myself, "it would be cool if I could visualize all the classes in the framework on my screen" but then I thought "what if there are more classes than there are pixels?"...

Anyway, it seems like something that mathematics might formalize in order to answer a question like, "given N pixels, how many Y would you possibly be able to visualize?"

I'd just like to know what to call this so I can Google it.

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Category theory? - If by information you mean structure, rather than some quantification thereof. –  alancalvitti Feb 8 '13 at 4:34

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Your question as you ask it seems to be a combinatorics question.

Based on your title, you might want to look into information theory.

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Information theory is a branch of math/computer science that has to do with limits on storing, compressing, and transferring information. This sounds like what you are asking about.

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