Jack M
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 Mar25 comment Sufficient rigor in proving $f(x)$ is continuous at the origin, for $f$ analog to the Dirichlet function. @Analysis Fix $\epsilon$. Then there exists a $\delta_1$ that works for $g$ and a $\delta_2$ that works for $h$. The smaller of the two works as the $\delta$ for $f$. Mar24 comment Number of triangles in a planar graph When you say "triangular region", do you mean complete subgraphs of three vertices? Mar24 comment How can I interpret the ratio $\frac{f(x_0)}{f'(x_0)}$? By "projected segment length", you mean $x_0-x_1$ (give or take a sign which I don't feel like working out), where $x_1$ is the $x$-coordinate at which the tangent line crosses the $x$-axis. Mar24 comment How to learn about the Rubik's Cube? On "Am I holding myself back if I refuse to read what other people have done before I work it out for myself", normally I would say yes, if we were talking about a major area of mathematics (for instance if you were refusing to read a textbook on number theory until you could derive quadratic reciprocity on your own), but if it's just solving a Rubik's cube then no, it's not a big deal. Mar24 awarded Popular Question Mar24 comment Cardinality of transcendental numbers Why is it a problem that transcendental and algebraic numbers can be complex? Mar24 answered Is it true that the splittings fields cannot be isomorphic? Mar24 answered Solve the following recurence relation. Mar24 answered Sufficient rigor in proving $f(x)$ is continuous at the origin, for $f$ analog to the Dirichlet function. Mar24 comment what is the answer about this function? For part (a) you can simply say that $f$ has an inverse, namely $-f$, and is therefore injective. Mar23 answered Solving a radical equation for real roots Mar22 comment What is the $100$-th term in the sequence $1,2,2,3,3,3,4,4,4,4\ldots$? @Henrik This is frankly a ridiculous complaint. It's perfectly clear what the asker meant. Mar22 comment Is there an area of study regarding why certain mathematical definitions are useful? Sort of. It's called History of Mathematics. Mar21 comment What is a good complex analysis textbook? I found Visual Complex Analysis to be utterly incomprehensible when I was trying to learn Complex Analysis. It's not just non-rigorous, it's barely even a textbook: theorems are indirectly hinted at rather than explicitly stated, definitions are non-existent and there didn't seem to be any proofs at all. Mar19 answered Is there a slowest divergent function? Mar19 revised Is this mapping an isomorphism? edited tags Mar18 answered Ring isomorphism (polynomials in one variable) Mar18 answered Base-n arithmetic and multi-dimensional matrices Mar17 comment Why did it take mathematicians so long to discover non-Euclidean geometry? @TonyK It's an accurate answer. Ancient geometers thought of a line as a line. Expecting ancient mathematicians to think in terms of undefined terms obeying formal laws is anachronistic. Mar17 comment Why did it take mathematicians so long to discover non-Euclidean geometry? @TonyK I think it cuts right to the heart of the fundamental problem with "why" questions. Any "why X" question implies that there is something surprising about X which needs to be explained. Whether or not this particular X is surprising is at best subjective, which I think makes the question somewhat unanswerable.