Thomas Klimpel
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 Jan 4 revised Is this a valid proposition? tried to add a short version without much preliminaries Jan 4 comment Is this a valid proposition? If you don't know "first order logic" (also known as predicate calculus), then my answer is not appropriate for you, and I doubt that "simpler terms" would help in this case. In that case, please forget immediately that I even dared to mention "modal logic". Even if you know "first order logic", it's better not to care too much about the "modal logic" part, because it's more of interest for philosophers. I could recommend you excellent books about logic in German. For English literature, Peter Smith wrote the excellent Teach Yourself Logic: A Study Guide! Jan 4 reviewed Reject Expected Value of SDE Jan 4 answered Is this a valid proposition? Jan 4 comment Is this a valid proposition? @Gina May I remind you that formula are allowed to contain free variables? A formula with no free variables is called a sentence. So if x is a constant, then yes it is a well-formed sentence. And to disappoint you even further, in first-order logic, the propositions are the formulas, i.e. there can be free variables. So the confusion is probably related to what "free variable" means in first-order logic. Jan 3 comment Are there intensional classes independent of the set universe? @CarlMummert The class of all sets certainly is a proper class, but is its "listing" of properties really independent of the set universe? In that case, the "listing" should probably be empty. But are the axioms of ZFC sufficient to ensure this? If not, is it even possible to give a c.e. axiom set that achieves this? If we drop the condition that the class has to be a proper class, we might also ask whether the hereditarily finite sets are purely intensional, i.e. whether the "listing" of their properties is independent of the set universe. I guess they are in ZFC, but that's another question. Jan 2 comment Are there intensional classes independent of the set universe? @LawrenceWong By purely extensional, I mean that the set can be defined by "listing" its elements, and its elements themselfes are also purely extensional. By "listing" its elements, I mean that the elements will be "the same" (up to isomorphism), independent of the set universe. Jan 2 reviewed Looks OK Find max: $\frac{a}{b+2a}+\frac{b}{c+2b}+\frac{c}{a+2c}$ Jan 2 reviewed Looks OK Find max: $M=\frac{a}{b^2+c^2+a}+\frac{b}{c^2+a^2+b}+\frac{c}{a^2+b^2+c}$ Jan 2 reviewed Looks OK Prove, that f is a linear map. Jan 1 revised Are there intensional classes independent of the set universe? The class of all sets with two elements is a nicer example of what worries me? Jan 1 asked Are there intensional classes independent of the set universe? Dec 19 comment meaning of differentiation of stochastic process @cabri61 Because Brownian motion is (in a suitable sense) nowhere differentiable, thinking about tangent lines won't help. However, if you understand the Stieltjes integral and the corresponding Stieltjes measure, then you might be able to appreciate an interpretation of $dX_t$ as a (stochastic) measure. (I say stochastic measure, because it's $dX_t(\omega)$, if we are careful about notation. I don't know whether $dX_t(\omega)$ is almost surely a Stieltjes measure for fixed $\omega$, but I guess not.) Dec 19 answered meaning of differentiation of stochastic process Dec 6 comment Is there a useful definition of minors for digraphs? @ShivaKintali Are you sure? No digraph in the infinite list contains a source or a sink. It seems to me that the digraph obtained via "Source Contraction" will contain at least one source, and I don't see how you will be able to get back to a source and sink free digraph. In addition, all contraction operations from the paper seem to be compatible with the notion of digraph minor used in the answer. Hence I would be surprised if the counterexample didn't apply. Dec 6 comment Is there a useful definition of minors for digraphs? Shiva Kintali introduces a paper about Forbidden Directed Minors and Kelly-width and announces "As mentioned in the paper, I have a series of upcoming papers (called Directed Minors) making progress towards a directed graph minor theorem (i.e., all digraphs are well-quasi-ordered by the directed minor relation)." It might be interesting to see whether the counterexample given under Edit 2 below also applies to his notion of directed minor relation. Dec 6 comment Is there a useful definition of minors for digraphs? The diploma thesis Über Minoren gerichteter Graphen by Steffen Seidler might be illuminating, especially if German is your first language. Nov 28 answered Should axioms be viewed as part of the signature? Nov 28 comment Is a groupoid a universal algebra? @HSN For general (universal) algebras, the kernel a morphism is a congruence instead of a normal subgroup. Both the quotient of an (universal) algebra by a congruence, and the quotient of a congruence by a sub-congruence are well defined. Nov 27 answered Is a groupoid a universal algebra?