Intereting Posts

Rapid approximation of $\tanh(x)$
Mrówka spaces are first-countable
Why Is a Function Defined As Having Only One Y-Value Output?
Eigenvalue decomposition of $D \, A \, D$ with $A$ symmetric and $D$ diagonal
Fibered products in $\mathsf {Set}$
How to find the minimum/maximum distance of a point from elipse
Group of order $3^a\cdot5\cdot11$ has a normal Sylow 3-group
coordinate ring questions
Group Law for an Elliptic curve
Product and Box Topologies
Is the localization of a PID a PID?
If $p$ is a positive multivariate polynomial, does $1/p$ have polynomial growth?
Irreducible polynomial in $\mathbb{F}_{p}$
$\ln r+\ln q=kr$ Isolating $r$
Same number of partitions of a certain type?

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.

- Is there a name for the “famous” inequality $1+x \leq e^x$?
- Proof of continuity of Thomae Function at irrationals.
- Fourier-Series of a part-wise defined function?
- Law of iterated logarithms for BM
- Convergence $I=\int_0^\infty \frac{\sin x}{x^s}dx$
- Has the polynomial distinct roots? How can I prove it?

- Which $f \in L^\infty$ are the Fourier transform of a bounded complex measure?
- Why is this sequence of equicontinuous functions uniformly bounded?
- Weak closure of $\{\sqrt n e_n|n\in \mathbb N\}$ and metrizability of weak topology
- Integral inequality (Cauchy-Schwarz)
- Limit of solution of linear system of ODEs as $t\to \infty$
- Minkowski Dimension of Special Cantor Set
- Convergence of the arithmetic mean
- Cardinality of a Hamel basis of $\ell_1(\mathbb{R})$
- Can we construct a function $f:\mathbb{R} \rightarrow \mathbb{R}$ such that it has intermediate value property and discontinuous everywhere?
- An infinite subset of the closed unit ball whose elements are more than distance 1 apart

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

- Having a plane equation equaled to zero for calculating its angle with another plane
- Run of $N$ successes before run of $k$ failures
- Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
- Finitely generated modules over PID
- Intuitive explanation of Cauchy's Integral Formula in Complex Analysis
- Why is pointwise continuity not useful in a general topological space?
- Explicit value for $\sum_{n=1}^{\infty} \left(\frac{1}{\sqrt{1}+\sqrt{2}+\dots+\sqrt{n}}\right)$
- Fourier transform of 1/cosh
- Solving $(z+1)^5 = z^5$
- Making an infinite generating function a finite one
- Possible ways to walk to school
- Proving the last part of Nested interval property implying Axiom of completeness
- What is the probability of randomly selecting $ n $ natural numbers, all pairwise coprime?
- Associativity of logical connectives
- How to prove Cauchy Criterion for limits