query: A continuous function taking natural numbers is constant
positive_passages.docid: 727
positive_passages.text: Prove that any continuous integer-valued function of a real variable is constant.
negative_passages.docid: 132478
negative_passages.text: Prove that continuous functions mapping irrationals to rationals must be constant
negative_passages.docid: 776
negative_passages.text: Entire function with positive real part is constant (no Picard)
negative_passages.docid: 71487
negative_passages.text: Real Analysis: Continuity of a Composition Function
negative_passages.docid: 111990
negative_passages.text: Continuous function from $(0, 1]$ onto $(0, 1)$?
negative_passages.docid: 154034
negative_passages.text: Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function.
negative_passages.docid: 97371
negative_passages.text: Proving a function is constant, under certain conditions?
negative_passages.docid: 39921
negative_passages.text: show that f is constant on I
negative_passages.docid: 126842
negative_passages.text: Fixed point in a continuous function
negative_passages.docid: 12523
negative_passages.text: Supremum of a Continuous Function is Continuous
negative_passages.docid: 2142
negative_passages.text: Finding a set of continuous functions with a certain property 2
negative_passages.docid: 147516
negative_passages.text: Continuous function whose right hand derivative equals 0 is constant?
negative_passages.docid: 130019
negative_passages.text: Function that is continuous only on the transcendental numbers
negative_passages.docid: 58664
negative_passages.text: Proving a function is continuous for a fixed variable
negative_passages.docid: 131992
negative_passages.text: A problem on continuous functions
negative_passages.docid: 18082
negative_passages.text: A continuous function that attains neither its minimum nor its maximum at any open interval is monotone
negative_passages.docid: 12240
negative_passages.text: Problem with a continuous function