query: Proof that a continuous function is zero
positive_passages.docid: 71071
positive_passages.text: Nonzero $f \in C([0, 1])$ for which $\int_0^1 f(x)x^n dx = 0$ for all $n$
negative_passages.docid: 12349
negative_passages.text: a construction of a continuous function from a normal space to [0,1]
negative_passages.docid: 80643
negative_passages.text: Show that f(x) defined on [0,infinity) R to is continuous at 0.
negative_passages.docid: 17234
negative_passages.text: Show that a continuous function has a fixed point
negative_passages.docid: 139763
negative_passages.text: A function takes every function value twice - proof it is not continuous
negative_passages.docid: 113975
negative_passages.text: Let $f:\mathbb{R}\to\mathbb{R}$, $f(kx)=f(x)$. Show that if $f$ is continuous at $0$ then $f$ is a Constant function
negative_passages.docid: 40576
negative_passages.text: Intermediate value property problem and continuous function
negative_passages.docid: 143174
negative_passages.text: property of continuous function
negative_passages.docid: 139744
negative_passages.text: For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
negative_passages.docid: 13852
negative_passages.text: Assume $f$ is a continuous one-to-one function over an interval. Prove that $f$ is strictly monotone
negative_passages.docid: 131000
negative_passages.text: A proof of a criterion of vanishing of a function.
negative_passages.docid: 46834
negative_passages.text: show that a distance function is continuous
negative_passages.docid: 149354
negative_passages.text: Proof of continuity $f(x+y) = f(x) + f(y)$
negative_passages.docid: 97104
negative_passages.text: Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
negative_passages.docid: 146707
negative_passages.text: Formally show that the set of continuous functions is not measurable
negative_passages.docid: 16743
negative_passages.text: Graph of real continuous function has measure zero
negative_passages.docid: 11158
negative_passages.text: Proof that a continuous function with $f(x) = f(x^2)$ is constant.