Charles Stewart
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 Feb18 awarded Notable Question Jan13 comment In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$? @epimorphic - I'm sorry: I managed to confuse myself about what was going on here; it is clear that Annix is not disposed to summarise the problems with his/her answer. You could provide an answer that starts with Annix's attempt at a solution, summarises your comments above to shows why the definition of dual numbers is incoherent, and concludes by saying Steven is right. (If you like, you could just cut and paste your last comment, and I'll fill in the rest.) Jan10 comment In dual numbers, what is the value of expressions $0^\varepsilon$ and $\varepsilon^{\varepsilon}$? +1: In view of the fact that, in comments, the qn of @epimorphic, ´What are i, j, and ϵ?´, has been answered, this answer is useful and concise. It would be improved further if the use Anixx has put these glyphs to were explained in the body of the answer. Jan9 comment Is $0$ a natural number? @Annix: I'm not sure why you wrote this comment. Are you claiming ignorance, authority, or something else altogether? Jan9 comment Solutions to functional equation $f(f(x))=x$ -1: flippant, incomplete. Your answer does not show that the class with this symmetry has any members other than those in the question Dec9 awarded Caucus Dec9 comment In plain language, what's the difference between two things that are 'equivalent', 'equal', and 'identical'? With ZFC, bijectivity is the same as having same cardinality, but often we care about equivalence as ordinality. If we care about "sets as trees", then bare equality is on topic. (+1: "types") Sep9 awarded Good Question Jul20 awarded Yearling Jul2 awarded Curious Jun24 comment Why an inconsistent formal system can prove everything? @Blaisorblade - if you mean that abstract syntax can solve the issue with substitution, then I guess that most mathematicians have little idea of the work done in this field. May1 awarded Pundit Apr4 reviewed Approve Matlab program of a finite sum that returns the result in a matrix Apr4 reviewed Approve Powers of permutation matrices. Apr3 awarded Custodian Apr3 reviewed Reject From centroid and two vertexes to find the missing vertex of a triangle. Apr2 comment What precisely is a vacuous truth? @MJD: I don't think much of the WP article. It doesn't link its definitions to the sources it lists, and it does not relate to well-known related topics. The claim 'A statement S is "vacuously true" if it resembles the statement $P \Rightarrow Q$, where P is known to be false' is unattributed, imprecise (resembles?, no outermost quantifier?, does "known" mean this is an epistemic claim?) and I would say is false (rather, vacuous truths "resemble" a special case of this form), and the well-known example is generally described as a paradox of material implication. Apr2 comment What is the antiderivative of $e^{-x^2}$ What you call the elementary functions, Hardy called the logarithmico-exponential functions: pp. 54-90 of plms.oxfordjournals.org/content/s2-10/1 Dec13 revised Basic Tautology Question right != left Dec13 answered Basic Tautology Question