query: Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be multiplicative. Is it exponential?
positive_passages.docid: 21891
positive_passages.text: If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
negative_passages.docid: 152841
negative_passages.text: I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
negative_passages.docid: 22890
negative_passages.text: Is it coherent to extend $\mathbb{R}$ with a reciprocal of $0$?
negative_passages.docid: 28520
negative_passages.text: Exponential or logarithm of a dimensionful quantity?
negative_passages.docid: 103550
negative_passages.text: Multiplicative Euclidean Function for an Euclidean Domain
negative_passages.docid: 135641
negative_passages.text: Algebraic independence of exponentials
negative_passages.docid: 84189
negative_passages.text: Is $\mathbb{C}$ equal to $\mathbb{R}^2$?
negative_passages.docid: 98696
negative_passages.text: Is the exponential map ever not injective?
negative_passages.docid: 63590
negative_passages.text: Let $g$ be a function from $(0, 1)$ to $\mathbb{R}$ and $\int_0^1 g^2(x)dx$ finite. Does this imply that $\int_0^1 g(x)dx$ is finite?
negative_passages.docid: 108115
negative_passages.text: If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
negative_passages.docid: 134699
negative_passages.text: Can *any* real polynomial be factored linearly (plus a constant) over $\mathbb{R}$?
negative_passages.docid: 33944
negative_passages.text: Describe $\mathbb{R}[x]/(x^{2}+ax+b)$ where $a,b \in \mathbb{R}$
negative_passages.docid: 141799
negative_passages.text: Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
negative_passages.docid: 117419
negative_passages.text: Why is $e^{x}$ not uniformly continuous on $\mathbb{R}$?
negative_passages.docid: 105772
negative_passages.text: Definition of $\mathbb{R}^\infty$
negative_passages.docid: 64708
negative_passages.text: Proof that exponential function's limit definition increases monotonically?
negative_passages.docid: 104413
negative_passages.text: Is the exponential of $-d$ a positive definite kernel for a general metric space $(X, d)$?