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Starbright Electric Bolt
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@nonphatic This is all subjective, but zero indexing is just overall better I think? It's true that you can get in trouble the way the authors have, but I'd blame that on the "a,...,b" notation. With indexes the way you suggest, the sentence at the end would have to end "iff for all 0 < i <= k:". And it's true that it's less clear if you aren't used to it, but I think it's just like switching to the metric system or etc.
@enkiv2 They both bring something important into focus!
@nonphatic ooh what question (i won't be able to answer it but I like questions)
However, this post of yours reminds me of a book I bet you'd like: https://archive.org/details/cattheory/mode/2up Category theory for [scientists | the sciences] (same book different edition, I think) by Spivak is all about treating categories as knowledge representations. It's meant to be introductory, too.
@natecull @charlag Cardinality (whether there are infinitely many of anything) is not relevant to the distinction between categories and graphs. Both categories and graphs can be finite or infinite, although in terms of what is studied infinite categories and finite graphs are more frequent. But not overwhelmingly in either case.
@natecull @charlag
1. Never; describing a category requires giving more information than is present in a description of its underlying graph.
2. No more or less than any other mathematical object.
3. Categories can be represented. A category is no more or less than two sets and four functions between products of those sets. You can represent functions either as a lookup table or as code that computes that function.
1. Never; describing a category requires giving more information than is present in a description of its underlying graph.
2. No more or less than any other mathematical object.
3. Categories can be represented. A category is no more or less than two sets and four functions between products of those sets. You can represent functions either as a lookup table or as code that computes that function.