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210:. Obviously the reason for that is precision, which is important also. But the problem is that a definition of an unfamiliar term is often given in terms of 2-3 other unfamiliar terms, which in turn are defined in terms of more unfamiliar terms, etc.. I find myself diving through several layers of dependency definitions -- each with a different wikipedia page -- just to unpack one definition. And the problem with specialized notation is that it is not even clear
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Semigroup theory is not commonly thought even to math PhDs, although they'd probably at least have heard of the definition. The page for semigroups does however formally define it. Your complaint doesn't seem have anything specific about this page, which should definitely not repeat the definition of a semigroup.
386:. So that section of the article should be expanded by instantiating those notions from a more accessible incarnation of a *-semigroup (like those mentioned in the lead). Alas, given the relative obscurity of the topic, the only treatments appear in graduate-level textbooks, so it may require a bit of
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As a case in point, I was just looking up the definition of "inverse relation" on wikipedia, and the explanation talked about a "semigroup with involution", so I had to look up that, which was defined in terms of a "semigroup", so I had to look up that page, which says that "A semigroup generalizes a
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As far as I can see a *-regular semigroup is purely and simply an inverse semigroup (the inversion need not be the only involutory anti-isomorphism but if a regular semigroup has an involutory anti-isomorphism then the inverses are unique and so it is an inverse semigroup, which is also a '-regular
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In general learning mathematics from
Knowledge is not a good idea if one is clueless about basics. I have to say that while it's possible to get a compsci PhD (even from MIT) without ever learning the definition of a semigroup, that doesn't imply mean the math pages here need a lot of changes.
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so those are a prerequisite in order to grasp what's going on there. (The axiomatic definition that follows doesn't help much.) Besides that, it's rather unfortunate (if I got this right) that *-regular semigroup doesn't just mean a *-semigroups that's also a regular semigroup. Due to the
264:, though of course they should be clearly noted as being imprecise. The key point in a plain language definition is to avoid domain-specific jargon. For example: "Roughly speaking, a foo is . . . ". And later: "More precisely, a foo is . . . " (with full rigor and jargon).
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Actually, that wasn't the case. The rewritten section explains the distinction (correctly, I hope). To get example 6 you need to take the quotient of the free monoid with involution by identifying every letter with its own involution/inverse.
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The study of these appears to have been motivated by some additional properties of the
Penrose-Moore inverse that aren't shared by *-semigroups at large. This section is the most newbie-unfriendly because is states things in terms of
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I hope the above suggestions are helpful and don't just sound like complaints. I know it is hard to write such things in widely understandable ways, and I very much appreciate the efforts of all editors who contribute. Thanks! --
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Well, a few pages later, Lawson covered that, so... I've added it. Also, it occurred to me that the *-semigroup of binary relations is a rather trivial case of the full linear monoid on binary matrices (i.e. over
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I have a PhD in
Computer Science, and I've certainly had reasonable exposure to math and logic over the years, but I find this article unbearably difficult to unpack. The main problem is the
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If correct then it should be clearly stated (and in consequence the Moore-Penrose inverse is just the inverse in an inverse semigroup, which should also be clearly stated).
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does that. I've actually spent a good number of minutes trying to phrase that in words, but I think it's a pretty pointless exercise.
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Also the lead of this page contains two examples that anyone with PhD in any science should have little trouble understanding.
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is trying to say that the only free semigroup with involution is basically the one where word reversal is the involution?
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think it is important to introduce the jargon that is used in the field, but it should be fairly clearly separated from
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Also, complaining is easy. I invite you try and explain the formula (xy)* = y*x* in plain
English. Not even the
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and precisely into the meaning of the term. The (possibly imprecise) plain language definition should be given
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they face the prospect of a deeply nested recursive traversal through many pages of jargon-filled definitions.
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Google-unfriendly name that *-regular semigroups have, it's hard to locate the relevant literature on them...
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providing a layman's (approximate) definition, so that readers can get the gist of what the term is about
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monoid", so I had to look up "monoid" . . . except that I gave up at that point. :( (Stack overflow?)
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Actually, while there are plenty of examples here for the basic notion, the section
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plain language definitions help enormously, even if they are imprecise
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Please make this article easier to understand by non-mathematicians!
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If I am wrong it would be good to mention a counter-example.
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Semigroup_with_involution#Free_semigroup_with_involution
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Semigroup_with_involution#Basic_concepts_and_properties
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