New posts in real-analysis

$f$ differentiable, $f(x)$ rational if $x$ rational; $f(x)$ irrational if $x$ irrational. Is $f$ a linear function?

continuity and $C^2$ solution of a series

On the Euler sum $\sum \limits_{n=1}^{\infty} \frac{H_n^{(4)} H_n^2}{n^6}$

Show $\lim_{h \to \ 0} \frac{f(x + 2h) - 2f(x+h) + f(x)}{h^{2}} = f''(x)$ Proof verification

$\frac{dS}{d\rho}$ Factor arising

Examples of statements that are true for real analytic functions but false for smooth functions

Asymptotic behaviour of sum over the inverse japanese symbol

Sum of two sequences of functions converging in measure still converges in measure

Continuous functions and intervals

Intuitively and graphically what does the inequality of the mean value mean?

$P$ is a monic polynomial of degree $n$ , then which are correct?

Convergence to function that is not measurable

Necessity of a hypothesis in the fundamental theorem of calculus

Limit of $\lim\limits_{n\to\infty} (1 + \frac{x_n}{n})^n$

Continuous function that take irrationals to rationals and vice-versa. [duplicate]

If $(f_n)\to f$ uniformly and $f_n$ is uniformly continuous for all $n$ then $f$ is uniformly continuous

Differentiability of product/composition of function

How does one prove that $e$ exists?

On the summation $\sum \limits_{n=1}^{\infty} \arctan \left ( \frac{1}{n^3+n^2+n+1} \right )$

Cardinality of the set of Riemann integrable functions on [0,1]