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# 134 Actions

 Mar25 revised Is the 'variable' in 'let $y=f(x)$' free, bound, or neither? added 560 characters in body Mar25 revised Is the 'variable' in 'let $y=f(x)$' free, bound, or neither? added 16 characters in body Mar25 revised Is the 'variable' in 'let $y=f(x)$' free, bound, or neither? added 16 characters in body Mar25 revised Is the 'variable' in 'let $y=f(x)$' free, bound, or neither? added 16 characters in body Mar25 revised Is the 'variable' in 'let $y=f(x)$' free, bound, or neither? added 167 characters in body Mar25 answered Is the 'variable' in 'let $y=f(x)$' free, bound, or neither? Mar24 accepted Superstructure with sets as atomic/base entities Mar24 answered Superstructure with sets as atomic/base entities Mar24 comment how to express the set of natural numbers in ZFC Another definition lets 0 be the empty set and n +1 be the union of n and {n}. Yet another (I think older) option is to define each n as the equivalence class of sets with cardinality n. The idea underlying these definitions is that a natural number is simply a member of the domain of a model of a certain theory. That is, it doesn't matter or make sense to ask what the objects themselves are; only how they relate to each other (i.e., the relations defined on them) is relevant. Mar23 comment Infinite Disjunctions and Conjunctions @Hayden, My reply was longish, so I edited it in above. Mar23 revised Infinite Disjunctions and Conjunctions added 1516 characters in body Mar23 answered Infinite Disjunctions and Conjunctions Mar23 comment First order logic with N quantifiers - the number of members in the domain matters for validity/consistency in this situation? It sounds like you might have an odd conception of quantifiers. Could you say what you think quantifiers are, how they work, or what your own reasoning about the answer is? Mar22 comment Predicate Logic Problem Your (b) is right. Why would (a) and (d) be different from (b), aside from the negation? Why do you think they are not also implications? Right now, (a) says that everything is a blue truck that Ross likes, and (d) says that everything is a person, neither of which is what you want to say. You need to put some of these predications in an antecedent (or some equivalent construction). Also, there is a typo in (c) -- you're missing Rachel. Mar21 revised Natural and formal languages added 152 characters in body Mar21 awarded Commentator Mar21 comment Natural and formal languages @RobertS.Barnes, I don't know if Boolos' book has solutions in it, but Hodges has complete solutions for every problem. The Boolos book is popular enough that you can find material online from courses that use it. For example, I just found this manual (by one of the authors) of hints for odd-#ed problems online: princeton.edu/~jburgess/ManualA.pdf Mar20 answered Natural and formal languages Mar20 comment How should I understand “$A$ unless $B$”? @Jack, I think it can mean either of those. I edited in further explanation to my answer. The reason that my answer is so horribly long is to try to convince you that there isn't a single logical translation of "A unless B". You cannot rely on a superficial analysis of the structure. You must also consider the meaning, and you must consider the meaning in context, which includes prior discourse, common knowledge, etc. And even then, you might still be left with ambiguity. That's natural language. Mar20 revised How should I understand “$A$ unless $B$”? added 7657 characters in body