query: A bijective function $f:\Bbb R\to [0, \infty)$ has infinitely many discontinuities.
positive_passages.docid: 22210
positive_passages.text: Points of discontinuity of a bijective function $f:\mathbb{R} \to [0,\infty)$
negative_passages.docid: 152784
negative_passages.text: $f \in {\mathscr R[a,b]} \implies f $ has infinitely many points of continuity.
negative_passages.docid: 27800
negative_passages.text: For continuous function $ f:\mathbb S^1 \to \mathbb R$ there exists uncountably many distinct points $x,y$ such that $f(x)=f(y)$
negative_passages.docid: 80643
negative_passages.text: Show that f(x) defined on [0,infinity) R to is continuous at 0.
negative_passages.docid: 104842
negative_passages.text: Let $X$ be uncountable. Then the set of injective functions $f\colon X \to \mathbb{R}$ has empty interior in $\mathscr{C}(X;\mathbb{R})$
negative_passages.docid: 92089
negative_passages.text: If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$
negative_passages.docid: 83446
negative_passages.text: bijective continuous function on $\mathbb R^n$ not homeomorphism?
negative_passages.docid: 93964
negative_passages.text: Proving that $f$ is a bijection from $N$x$N$ to $N$.
negative_passages.docid: 90685
negative_passages.text: The composition of non-linear entire functions with no fixed points has infinitely many fixed points.
negative_passages.docid: 146436
negative_passages.text: Cardinality of the set of bijective functions on $\mathbb{N}$?
negative_passages.docid: 150346
negative_passages.text: If $f$ is an increasing function defined on $[a,b]$ . Then, $f$ has countable number of discontinuities
negative_passages.docid: 19072
negative_passages.text: $\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?
negative_passages.docid: 55679
negative_passages.text: Does there exist a continuous function from [0,1] to R that has uncountably many local maxima?
negative_passages.docid: 132868
negative_passages.text: Bijection between an infinite set and its union of a countably infinite set
negative_passages.docid: 60700
negative_passages.text: Continuity of a function to the integers
negative_passages.docid: 105772
negative_passages.text: Definition of $\mathbb{R}^\infty$
negative_passages.docid: 146306
negative_passages.text: A continuous surjective function from $(0,1]$ onto $[0,1]$