Newbetuts

Alternate proofs (other than diagonalization and topological nested sets) for uncountability of the reals?

Is D a borel subset?

if $Ax^2+Bxy+Cy^2$ is positive definite, then $A>0$ and $B^2-4AC<0$

Logarithm integral with golden ratio $\int^1_0 \frac{\log(1+\phi x^2)}{1+x}\, dx$

Motivation of Weierstrass-approximation Theorem?

Convex function with non-symmetric Hessian

Show $\int_0^\infty f\left(x+\frac{1}{x}\right)\,\frac{\ln x}{x}\,dx=0$ if $f(x)$ is a bounded non-negative function

Example of Converge in measure, but not converge point-wise a.e.?

Does pointwise convergence against a continuous function imply uniform convergence?

Does continuity always imply integrability?

Fixed point of a monotone on [0,1].

An inequality of $L^p$ norms of linear combinations of characteristic functions of balls

Is there a "one-line" proof of $x<y\Rightarrow x^n<y^n$ (for $n$ an odd natural number)?

Why is Axiom of Choice "a convenient and safe labour-saving device"?

Dirac measures are extreme points of unit ball of $C(K)^*$.

How is the discrete metric continuous?

New posts in real-analysis

Evaluating $ \lim_{n\rightarrow\infty} n \int_{0}^{1} \frac{{x}^{n-2}}{{x}^{2n}+x^n+1} \mbox {d}x$

A Continuous Nowhere-Differentiable Function

A proof of a property of limits

Help with evaluating a sum

Alternate proofs (other than diagonalization and topological nested sets) for uncountability of the reals?

Is D a borel subset?

if $Ax^2+Bxy+Cy^2$ is positive definite, then $A>0$ and $B^2-4AC<0$

Logarithm integral with golden ratio $\int^1_0 \frac{\log(1+\phi x^2)}{1+x}\, dx$

Motivation of Weierstrass-approximation Theorem?

Convex function with non-symmetric Hessian

Show $\int_0^\infty f\left(x+\frac{1}{x}\right)\,\frac{\ln x}{x}\,dx=0$ if $f(x)$ is a bounded non-negative function

Example of Converge in measure, but not converge point-wise a.e.?

Does pointwise convergence against a continuous function imply uniform convergence?

Does continuity always imply integrability?

Fixed point of a monotone on [0,1].

An inequality of $L^p$ norms of linear combinations of characteristic functions of balls

Is there a "one-line" proof of $x<y\Rightarrow x^n<y^n$ (for $n$ an odd natural number)?

Why is Axiom of Choice "a convenient and safe labour-saving device"?

Dirac measures are extreme points of unit ball of $C(K)^*$.

How is the discrete metric continuous?