query: Intuition of definition of degree of function $\deg(f)=\widetilde f(1)$
positive_passages.docid: 153052
positive_passages.text: What does the degree of a loop in $S^1$ means *intuitively?
negative_passages.docid: 69334
negative_passages.text: How to find degree of a differential equation.
negative_passages.docid: 34077
negative_passages.text: Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.
negative_passages.docid: 51612
negative_passages.text: Question About Notation In Field Theory $F(x)$ vs. $F[x]$
negative_passages.docid: 109159
negative_passages.text: What's the intuition behind $(\exists y)(\mathscr{C}(y)\supset\mathscr{D})\supset((\forall x)\mathscr{C}(x)\supset\mathscr{D})$
negative_passages.docid: 68746
negative_passages.text: What is $f(f^{-1}(A))$?
negative_passages.docid: 58597
negative_passages.text: A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
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: 21954
negative_passages.text: A question about $f(x)\equiv 0$
negative_passages.docid: 21301
negative_passages.text: If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$
negative_passages.docid: 104263
negative_passages.text: How to show that $f'(x)<2f(x)$
negative_passages.docid: 148545
negative_passages.text: Degree of interpolation polynomial
negative_passages.docid: 60520
negative_passages.text: Upper bound for $|f(0)|$ based on its behavior within the unit disk.
negative_passages.docid: 33598
negative_passages.text: Deduce function f from integral
negative_passages.docid: 85743
negative_passages.text: Consequences of Degree Theory
negative_passages.docid: 108115
negative_passages.text: If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
negative_passages.docid: 144323
negative_passages.text: Differentiation of a function