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Mar
25
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 $f$.
Mar
24
comment Number of triangles in a planar graph
When you say "triangular region", do you mean complete subgraphs of three vertices?
Mar
24
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.
Mar
24
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.
Mar
24
awarded  Popular Question
Mar
24
comment Cardinality of transcendental numbers
Why is it a problem that transcendental and algebraic numbers can be complex?
Mar
24
answered Is it true that the splittings fields cannot be isomorphic?
Mar
24
answered Solve the following recurence relation.
Mar
24
answered Sufficient rigor in proving $f(x)$ is continuous at the origin, for $f$ analog to the Dirichlet function.
Mar
24
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.
Mar
23
answered Solving a radical equation for real roots
Mar
22
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.
Mar
22
comment Is there an area of study regarding why certain mathematical definitions are useful?
Sort of. It's called History of Mathematics.
Mar
21
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.
Mar
19
answered Is there a slowest divergent function?
Mar
19
revised Is this mapping an isomorphism?
edited tags
Mar
18
answered Ring isomorphism (polynomials in one variable)
Mar
18
answered Base-n arithmetic and multi-dimensional matrices
Mar
17
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.
Mar
17
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.