query: prove that it's a constant function
positive_passages.docid: 26388
positive_passages.text: proof that function is constant
negative_passages.docid: 40208
negative_passages.text: Locally Constant Functions on Connected Spaces are Constant
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: 121771
negative_passages.text: Proof $f(x)\equiv 0$
negative_passages.docid: 32789
negative_passages.text: Show bounded harmonic function on $\mathbb{C}$ is constant.
negative_passages.docid: 63255
negative_passages.text: Proving an entire, complex function with below bounded modulus is constant.
negative_passages.docid: 54729
negative_passages.text: Prove that $f$ has a fixed point .
negative_passages.docid: 106290
negative_passages.text: Prove a function is constant. (complex analysis)
negative_passages.docid: 53497
negative_passages.text: Prove that the function is continuous and differentiable (not as easy as it sounds imo)
negative_passages.docid: 110112
negative_passages.text: Proving a function is Lipschitz continuous
negative_passages.docid: 153855
negative_passages.text: Complex analysis, showing a function is constant
negative_passages.docid: 47474
negative_passages.text: Proving $|f(z)|$ is constant on the boundary of a domain implies $f$ is a constant function
negative_passages.docid: 86517
negative_passages.text: If $|f(z)|\le |g(z)|$, can we say $f$ is constant?
negative_passages.docid: 727
negative_passages.text: Prove that any continuous integer-valued function of a real variable is constant.
negative_passages.docid: 100740
negative_passages.text: proof of that a continuous function has a fixed point
negative_passages.docid: 111756
negative_passages.text: How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
negative_passages.docid: 39921
negative_passages.text: show that f is constant on I