Intereting Posts

What's wrong with my solution for the birthday problem?
Let A be a non-empty set, and p an equivalence relation on A . Let a , b be an element of A . Prove that = is equivalent to apb
What is a good text in intermediate set theory?
Distribution of dot product?
Characterizing Dense Subgroups of the Reals
How do people who study intensely abstract mathematics “imagine” or understand the concepts they are studying or being taught?
If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$
Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$
A fast factorization method for Mersenne numbers
Probability of the Center of a Square Being Contained in A Triangle With Vertices on its Boundary
Calculate Point Coordinates
Do you need real analysis to understand complex analysis?
Erwin Kreyszig's Introductory Functional Analysis With Applications, Section 2.8, Problem 3: What is the norm of this functional?
How to derive the law of cosines without the pythagorean theorem
Literature on group theory of Rubik's Cube

Let $u$ be the solution of the equation $$e^x \log(x)=1$$

Is $u$ rational, irrational algebraic or transcendental?

$u$ seems to be transcendental, but I cannot prove it.

- Non-existence of irrational numbers?
- Can $\pi$ be a root of a polynomial under special cases?
- Is the sum of an algebraic and transcendental complex number transcendental?
- “The Galois group of $\pi$ is $\mathbb{Z}$”
- Is $ 0.112123123412345123456\dots $ algebraic or transcendental?
- For integer $k > 1$, is $\sum_{i=0}^{\infty} 1/k^{2^i}$ transcendental or algebraic, or unknown?

Perhaps, someone has an idea.

- Deciding whether $2^{\sqrt2}$ is irrational/transcendental
- Prove that $\pi$ is a transcendental number
- Reciproc of the Lindemann theorem and the arc cosine of the golden ratio
- Can $\pi$ be a root of a polynomial under special cases?
- For integer $k > 1$, is $\sum_{i=0}^{\infty} 1/k^{2^i}$ transcendental or algebraic, or unknown?
- Is $\{\tan(x) : x\in \mathbb{Q}\}$ a group under addition?
- Is the positive root of the equation $x^{x^x}=2$, $x=1.47668433…$ a transcendental number?
- Can permutating the digits of an irrational/transcendental number give any other such number?
- What are examples of unexpected algebraic numbers of high degree occured in some math problems?
- Every Real number is expressible in terms of differences of two transcendentals

- Schur skew functions
- If $|a| = 12, |b| = 22$ and $\langle a \rangle\cap \langle b\rangle \ne e$, prove that $a^6 = b^{11}$
- Understanding the proof that $L_\infty$ norm is equal to $\max\{f(x_i)\}$
- How do I determine if a point is within a rhombus?
- Verify $\int\sec x\ dx=\frac12 \ln \left\lvert\frac{1+\sin x}{1-\sin x}\right\rvert + C$
- How many different subsets of a $10$-element set are there where the subsets have at most $9$ elements?
- On Galois groups and $\int_{-\infty}^{\infty} \frac{x^2}{x^{10} – x^9 + 5x^8 – 2x^7 + 16x^6 – 7x^5 + 20x^4 + x^3 + 12x^2 – 3x + 1}\,dx$
- Jordan normal form and invertible matrix of generalized eigenvectors proof
- In-place inversion of large matrices
- Is the sum of all natural numbers $-\frac{1}{12}$?
- How do we prove the existence of uncountably many transcendental numbers?
- How (possibly) many subfields does $\mathbb{F}$ has that extend $\mathbb{Q}$?
- Proving $|f(z)|$ is constant on the boundary of a domain implies $f$ is a constant function
- Computing information about a Lie algebra from cartan matrix
- Prove that a group of order 3 must be cyclic.