I'll see if I can summarize this. Start with a notion of natural numbers, what do they mean? If we think of them as "sizes" of sets, we can generalize a bit. From there, we have equivalent notions of + and × that work with this concept.
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Then, when we write a+b or a×b, we're talking about the size of some other set. From there, we csn generalize a bit and "kick" this idea into a more abstract space using a key concept. By doing so, we can not only prove the distributed law as commonly known...
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...but in fact develop an equivalent such law for any other branch of mathematics with operations similar to + and ×. This turns out to be a bit like killing a mosquito with a cannon and accidentally discovering a treasure chest behind the wall.
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Pretty sure you didn't make it any clearer for 90% of the people out there. Hope it ends up online somewhere.
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pdf in thread!
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thanks
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