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spinosarus123
  • Member for 2 years, 9 months
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10 votes
Accepted

Why it is not enough to define a basis as a set of linearly independent vectors?

7 votes

Abstract Manifolds - Is $\mathbb R^m$ only a $C^1$ manifold?

6 votes
Accepted

Is this proof of "$a\neq0\Rightarrow a^{-1}\neq0$" valid?

6 votes
Accepted

Compactness of a set of functions on an infinite-dimensional function space

4 votes

Find all entire functions that satisfy the following equality

3 votes
Accepted

Lack of Existence for Entire Function such that $f(z)^2 + z^2 = 1$

3 votes
Accepted

Let $F \supset K \supset L$ be fields with orders less than 100 and do not include an element $x\neq 1$ that $x^5=1$. Find the order of $F$.

3 votes

Sum of $\sum^\infty_ \mathrm{n=0} a_nx^n$

3 votes
Accepted

If $f$ is continuous at $a$, then $\lim_{r\to 0^+} \frac{1}{\text{vol}(B_r(a))} \int_{B_r(a)} f\, dV=f(a)$.

3 votes

What is the constant function, exactly?

3 votes

Does choosing a branch cut determine what values for a multivalued function will make it single-valued?

3 votes
Accepted

How does the triangle inequality prove continuous?

3 votes

There are infinitely many k such that $p_{k+1} - p_{k} >2$

2 votes
Accepted

Definition of derivative confusion.

2 votes
Accepted

Is $x^2=y^2$ a symmetric relation?

2 votes

Question about a comment in my analysis book (differentiation)

2 votes

Abstract algebra book for slightly advanced beginner

2 votes

What is a rigorous proof of the topological equivalence between a donut and a coffee mug?

2 votes
Accepted

Is there an ambiguity in the definition of the limit that allows convergence to multiple values?

2 votes

The proof that if f(x) is continuous at x=c, then 1/f(x) is continuous at x=c

2 votes
Accepted

Does this guarantee invertibility in higher-dimensional functions?

2 votes

Can Cauchy's Theorem be used to solve a contour integral with singularities?

2 votes
Accepted

Inequality of product of inner products

2 votes
Accepted

Let $f,g:D\to\Bbb R,$ such that $f$ is continuous at $c$ and $\lim_{x\to\infty}g(x)=c,$ then, $\lim_{x\to\infty}f\circ g(x)=f(c).$

2 votes

$\displaystyle{\lim_{x \to 0^+} f'(x) = \lim_{x \to 0^-} f'(x)}$ imples $f$ differentiable at $0$?

2 votes

Why my solution was wrong (geometric series)?

2 votes

Defining subsets

1 vote
Accepted

Product of holomorphic and nonholomorphic function

1 vote
Accepted

Calculate integral with complex numbers over circle

1 vote

If an entire function $f$ can be written as a polynomial in a ball around $z_0$ for every $z_0 \in \mathbb{C}$, then $f$ is actually a polynomial.