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1d
comment Is the subset $[0, \sqrt2] ∩\mathbb{Q} ⊂ \mathbb{Q}$ closed, bounded, compact?
As stated in another comment, your answer is incorrect. This set is closed in the rationals.
Nov
23
comment Prove $x \geq \sin x$ on $[0,\pi/4]$
There's no need to phrase this as a proof by contradiction. Your approach shows directly that $f(x) \ge 0$ for any $x \in [0,\pi/4]$.
Nov
14
comment Evaluate the surface integral from the paraboloid
Why would that not be possible?
Nov
11
comment An Application of Intermediate Value Theorem
But you're not allowed to choose $b$, it's fixed at the beginning of the problem before any $c$ and $d$ enter the picture. What you would need to know in order to apply the Intermediate Value Theorem is that for any $b > 0$ there exist $c$ and $d$ such that $c^n < b < d^n$.
Nov
11
comment An Application of Intermediate Value Theorem
What do you mean by "By Archimedean Property of reals, we can find $f(c) < b < f(d)$"?
Nov
10
comment $3\times3$ matrix with 5 eigenvectors?
If there is any eigenvector at all, there will always be infinitely many.
Nov
9
comment Searching for the most elementary proof of a theorem in linear algebra
Would not the process of "exchanging basis elements one by one" essentially reproduce the proof of the given claim which is likely in the OP's book?
Nov
9
comment How to tackle a research journal - level course in Lie Theory and Representation Theory?
Sorry, I don't understand what you mean by "research journal" level course, and what you describe sounds like every graduate course in mathematics I ever took. Can you clarify? Do you have the necessary background for the course?
Nov
7
comment Finding a solution given the derivative and an interval.
Nowhere in your question do you specify the equation you're wanting to show has a solution, can you clarify?
Nov
3
comment Symbol for 'When …'
In any kind of formal setting it is usually preferred to write these things out, so "when" wins. That is, you would likely not even see "$\Rightarrow$" in formal writing, but instead "implies" or written as an if-then statement. Again, it depends on your audience.
Nov
3
comment Symbol for 'When …'
In other words, it is not very often that you hear "$Q$ is implied by $P$" as opposed to "$P$ implies $Q$", although it does happen.
Nov
3
comment Symbol for 'When …'
It will likely be understood by anyone who knows what an implication is, but I would not say that it is standard notation. Best to check with whatever audience you're writing this for whether or not it would be understood.
Nov
3
answered Symbol for 'When …'
Nov
2
comment Finding the Curl of a vector field. (Vector calculus)
If you compute the curl of what you obtained, do you get the original field?
Nov
1
answered Name for the set {Mv : |v| = 1}
Oct
22
comment Row reduction and the characteristic polynomial of a matrix
Are you wanting to row-reduce $A$ or $\lambda I-A$?
Oct
18
comment Why must every vector in V belongs to one of the generalised eigenspaces of $T: V \to V?$
It is not true that every vector in $V$ belongs to a generalized eigenspace.
Oct
2
comment Showing that a map, $R:\mathbb{R}^n\rightarrow\mathbb{R}^n$ can be represented by an orthogonal matrix.
This matrix is not orthogonal, and you also seem to assume that $n=3$.
Sep
27
comment What is the difference between a Limit and Derivative?
A derivative is a specific type of limit, but "limit" is a much more general notion.
Sep
25
comment An estimate for the lower Riemann sum for the derivative of a differentiable function
It is not assumed that $f'$ is integrable.