Intereting Posts

Beside transcendental or uncomputable numbers what other types of numbers are there?
The constant of integration during integration by parts
Example of Erdos-Szekeres bound being tight
Integration by Parts implies U-substitution?
Strategies to find the set of functions $f:\mathbb{R}\to\mathbb{R}$ which satisfy a given functional equation
Relationship between subrings and ideals
Continuity of normalized displacement vector for a smooth closed curve
Extending partial sums of the Taylor series of $e^x$ to a smooth function on $\mathbb{R}^2$?
Alternate proof for $a^2+b^2+c^2\le 9R^2$
Counting all possible board positions in Quoridor
Can it happen that the image of a functor is not a category?
Stirling Number of second kind (unsigned) and binomial coefficient, proof of equality?
Derangement of n elements
Are two mathematically alike functions equal?
Sum of Binomial random variable CDF

I can prove the converse of it, but I cannot do this one. Here is the problem:

Prove that the implicit function theorem implies the inverse function theorem.

- Integral $\int \sqrt{x+\sqrt{x^2+2}}dx$
- Can we use this formula for a certain indeterminate limit $1^{+\infty}$?
- How do you show that $l_p \subset l_q$ for $p \leq q$?
- Is this proof of the fundamental theorem of calculus correct?
- Identifying recursive polynomials
- equation involving the integral of the modular function of a topological group

- Basic question about $\sup_{x\neq 0}{} \frac{\|Ax\|}{\|x\|} = \sup_{\|x\| = 1}{\|Ax\|} $, $x \in\mathbb{R}^n$
- Quaternions as a counterexample to the Gelfand–Mazur theorem
- Why isn't an odd improper integral equal to zero
- Adjoint of an operator on $L^2$
- A convex subset of a Hilbert space
- separable Banach space with Banach-Mazur distances to $\ell_2^n$ bounded must be isomorphic to $\ell_2$?
- about limit of a sequence
- Spectrum of idempotent element
- Are the coordinate functions of a Hamel basis for an infinite dimensional Banach space discontinuous?
- In a $p$-adic vector space, closest point on (and distance from) a plane to a given point?

For $f : \mathbb{R}^n \to \mathbb{R}^n$, consider $F : \mathbb{R}^n\times\mathbb{R}^n \to \mathbb{R}^n$ given by $F({\bf x}, {\bf y}) = f({\bf y}) – {\bf x}$.

- A Curious binomial identity
- Approximation in Sobolev Spaces
- Prove $\frac{\sec{A}+\csc{A}}{\tan{A} + \cot{A}} = \sin{A} + \cos{A}$ and $\cot{A} + \frac{\sin{A}}{1 + \cos{A}} = \csc{A}$
- Understanding precisely the dot product…
- Is $\sum \sin{\frac{\pi}{n}}$ convergent?
- If matrix A is invertible, is it diagonalizable as well?
- moment inequality
- Is there a computer program that does diagram chases?
- prove the divergence of cauchy product of convergent series $a_{n}:=b_{n}:=\dfrac{(-1)^n}{\sqrt{n+1}}$
- Useful reformulation of Goldbach's conjecture?
- Is a finite commutative ring with no zero-divisors always equal to the ideal generated by any of its nonzero elements
- Borel algebra mod meagre sets vs. Borel algebra mod sets of measure zero
- How to prove following integral equality?
- What happens if I toss a coin with decreasing probability to get a head?
- Number of nonnegative integral solutions of $x_1 + x_2 + \cdots + x_k = n$