Questions tagged [soft-question]
For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.
12,410 questions
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How did you learn to think like an analyst? [closed]
Just a little background, I am junior studying mathematics at my college, and I have previously taken an introductory abstract algebra course, only covering groups, and two courses in Real Analysis, ...
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Is it ok to identify $L\subset\mathbb{R}\times\mathbb{R}$ with $\mathbb{R}$ and describe the topology on $L$ in terms of the topology on $\mathbb{R}$?
I am reading "Topology Second Edition" by James R. Munkres.
Munkres does not define homeomorphisms between topological spaces in the pages leading up to the following Exercise 8. What kind ...
- 10.4k
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Can you prove equality of two expressions by setting them equal in an equation? [closed]
Suppose I have two expressions, and I wish to prove that they are equal to each other. Must I perform algebraic operations on one of the expressions in an attempt to reach the other one? Or perhaps ...
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Will Fermat's Last Theorem and Wiles' Theory become part of undergraduate courses in the future? [closed]
Our abstract algebra has been firmly connected to the works of Ruffini, Abel and Galois about solving polynomials by radicals, I want to know is Wiles work about Fermat last theorem essential enough ...
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What are some proofs that you find to be amusing in some way? [closed]
For example, I think the proof of the Rice-Shapiro Theorem is kind of funny (specifically the "downward" part of the proof).
Let $S$ be a set of partial recursive functions with a ...
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Practical and historical role of Jordan measure [migrated]
In my earlier questions, the proofs given by Asigan and D.R. showed that the Jordan outer/inner measure of the subgraph $[0,f]$ and the Darboux upper/lower integrals of $f$ are essentially the same ...
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Want an explanation of using Extreme Value theorem to prove Rolle's theorem(solved)
I'm confused about using extreme value theorem here
proof from
https://mathcenter.oxford.emory.edu/site/math111/proofs/rollesTheorem/
Consider the two cases that could occur:
Case 1:
$f(x) = 0$ for ...
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Counter example to differentiation under the integral sign [closed]
If we have the integral in $\mathbb{R}$: $$\int_\mathbb{R}1_{[0,x]}(t)dt $$
Where $dt$ denotes the Lebesgue measure. Is differentiable for a.e $t$, (away from $x$), is clearly dominated for all $x$. ...
Lucca rodriguez
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Examples of propositions for which there is $N,N'$ s.t. the proposition is true for $1\leq n\leq N,$ false if $N< n\leq N',$ true if $n>N'?$
I know of examples of "natural" (i.e. not contrived) propositions which are false for the first few, for example, $3,$ values of $n,$ but are true thereafter, for example, for all $n\geq 4.$ ...
- 25.2k
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Series that is known to converge/diverge but for which all these standard tests are inconclusive .
I have noticed that nearly every series I have been asked to analyze its convergence or divergence can be handled by the usual collection of tests: the limit test, Cauchy condensation, the integral ...
- 9,329
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Notation for mapping angle/axis to unit quaternion
I'm an engineer writing some documentation with maths notation.
In one expression I'm writing, I need to map an axis $A \in S^2$ and an angle $\alpha \in \mathbb{R}$ to a unit quaternion representing ...
- 487
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Mathematics for Perspective Drawing
I am an undergraduate math major who likes to draw, and I would like to learn the math behind perspective drawing.
I recently watched this video: Everything about Perspective & Correct ...
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On notational conventions between Bott & Tu Vs. Lee for differential forms
Since I have been introduced to differential forms, I have seen (naively speaking) when you apply the exterior derivative, you "wedge" together one additional $d$ of the variable in question ...
- 5,290
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Why do we say "Let $ ABC$ be a triangle"? [closed]
My question is not just about let $ ABC$ be a triangle but rahter about all the mathematical statements where we say "Let some XYZ be PQR"
so why we? I mean even without let or suppose if ...
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Investigating the topological properties of a quotient space of $\mathbb R^2$, given by identification of irrational lines through $0$.
My question is about a very erratic quotient space. I encountered this space in some topology exercise. The space $X$ is described in the following:
Let $\mathbb R^2=\{(x,y):x,y\in \mathbb R\} $ be ...
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