Proving that a limit of piecewise function defined for rationals and irrationals does not exist
122762
Proving that the limit doesn't exist for $x$ other than $0$
65895
Irrationality proofs not by contradiction
86988
Cardinality of the Irrationals
113450
Construction of a function which is not the pointwise limit of a sequence of continuous functions
138446
Proving that there exists an irrational number in between any given real numbers
2167
Find the limit $\lim\limits_{x\to \infty}(e^{-x}+2\cos3x)$, or show that it does not exist.
60722
Why does Cantor's diagonal argument not work for rational numbers?
125860
Showing that $\lim\limits_{n\to\infty}x_n$ exists, where $x_{n} = \sqrt{1 + \sqrt{2 + \sqrt{3 + ...+\sqrt{n}}}}$
141937
Prove that the $\lim_{(x,y) \to (0,0)}h(x,y)$ Does not Exist using Polar Coordinates
87131
Discontinuous at rationals and differentiable at irrationals?
121085
Showing that $\lim\limits_{x \rightarrow 0} \frac{1}{x}$ does not exist.
24817
Prove continuity on a function at every irrational point and discontinuity at every rational point.
133231
Discontinuity of Thomae Function on $\mathbb{Q}$
139622
Generator of rational functions unchanged under $\sigma(X) = X + 1$
84987
Two paths that show that $\frac{x-y}{x^2 + y^2}$ has no limit when $(x,y) \rightarrow (0,0)$
21670
Why does an infinite limit not exist?
124997
finding examples for a non negative and continuous function for which the infinite integral is finite but the limit at infinity doesn't exist