query: Example: Continuous function having a limit along every arithmetic sequence but having no limit over the reals
positive_passages.docid: 28413
positive_passages.text: Limit of a continuous function
negative_passages.docid: 40562
negative_passages.text: For $f :\mathbb{R} \rightarrow \mathbb{R}\displaystyle$ we have ${\lim_{n \to +\infty} f(x+n) =0}$ almost everywhere
negative_passages.docid: 12349
negative_passages.text: a construction of a continuous function from a normal space to [0,1]
negative_passages.docid: 148931
negative_passages.text: Constructing a function that is continuous and has a max on an open interval, but is not necessarily increasing immediately to the left of the max.
negative_passages.docid: 100436
negative_passages.text: Examples of nowhere continuous functions
negative_passages.docid: 158309
negative_passages.text: Find a function that is continuous only on rationals
negative_passages.docid: 111990
negative_passages.text: Continuous function from $(0, 1]$ onto $(0, 1)$?
negative_passages.docid: 129087
negative_passages.text: Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
negative_passages.docid: 103241
negative_passages.text: A function that is continuous at the origin but not differentiable there
negative_passages.docid: 33330
negative_passages.text: Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
negative_passages.docid: 125754
negative_passages.text: Proving or disproving a statement about continuity and limits
negative_passages.docid: 24271
negative_passages.text: Limit of absolute value of sequence
negative_passages.docid: 92734
negative_passages.text: Existence of a sequence of continuous functions convergent pointwise to the indicator function of irrational numbers
negative_passages.docid: 63701
negative_passages.text: An example of a regular function over an open set
negative_passages.docid: 11586
negative_passages.text: Sequences of Real Numbers in a closed bounded interval
negative_passages.docid: 21269
negative_passages.text: Bijective continuous function between $(0 ,\infty)$ and $\mathbb{R}$.
negative_passages.docid: 113740
negative_passages.text: Find a uniformly continuous function such that $a_{n+1}=f(a_n)$