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1d
comment Proving Euler's formula without calculus
How are you defining $e^{ix}$?
Dec
18
comment Determinant: Continuity
How are you defining the determinant?
Dec
17
comment Differentiablility of a function
Your use of L'Hopital's rule is invalid: the limit after you differentiate numerator and denominator must exist in order for L'Hopital to be applicable.
Dec
15
comment Complex Analysis using derivatives
I see nothing whatsoever about derivatives in the linked-to article.
Dec
11
comment Restrictive definition of diagonalizable matrix
If every matrix can be "diagonalized" according to your definition, then what is the point of even introducing that definition?
Dec
11
comment Linear transformation ker and image
Neither of your candidate vectors for a basis of the kernel are actually in the kernel.
Dec
10
awarded  Caucus
Dec
5
comment Proof of an inverse
Show that $F$ is bijective.
Dec
5
comment Is a homomorphisim one-to-one or onto?
Smooth functions are continuous, hence any smooth function has an antiderivative.
Dec
5
comment Is a homomorphisim one-to-one or onto?
Hmmm, it seems I deleted my comment by mistake. To recap: the function $f$ defined by $f(x) = \int_0^x e^{t^2}\,dt$ has derivative $f'(x) = e^{x^2}$, and more generally any continuous function has an antiderivative by a similar argument.
Dec
2
comment orthogonal subspaces in $\mathbb R^2$
Your impression is incorrect: a set consisting of a single vector is considered to be orthogonal since it is true that any vector in this set is orthogonal to anything else in it, simply because there is no other vector in the set on which to test this condition.
Dec
1
answered Vector dot product = 0 for perpendicular vectors
Nov
27
comment Triple Integrals: Conversion
You're being asked only to sketch the region of integration, not to actually compute the integral.
Nov
25
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?