query: Span of Polynomials in $\mathcal{C}(\mathbb{R})$
positive_passages.docid: 154625
positive_passages.text: $\operatorname{span}(x^0, x^1, x^2,\cdots)$ and the vector space of all real valued continuous functions on $\Bbb R$
negative_passages.docid: 48260
negative_passages.text: If $R=K[X]/(X^n)$, can represent any element as polynomial with degree $<n$
negative_passages.docid: 55509
negative_passages.text: Factor a polynomial over the reals
negative_passages.docid: 84189
negative_passages.text: Is $\mathbb{C}$ equal to $\mathbb{R}^2$?
negative_passages.docid: 90055
negative_passages.text: Show that $\mathcal P(x)\notin x$
negative_passages.docid: 43282
negative_passages.text: Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
negative_passages.docid: 44704
negative_passages.text: familly of Radially open sets in $\mathbb{R}^2$
negative_passages.docid: 107389
negative_passages.text: Show that the vector space of real functions is not finitely spanned
negative_passages.docid: 31710
negative_passages.text: Show that $\mathcal{J}=\{[a, a+1) \mid a \in \mathbb{R}\}$ generates the Borel set of $\mathbb{R}$
negative_passages.docid: 44685
negative_passages.text: Inner product on $C(\mathbb R)$
negative_passages.docid: 114146
negative_passages.text: Polynomial in $n$ variables
negative_passages.docid: 62134
negative_passages.text: Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots
negative_passages.docid: 115502
negative_passages.text: Analogue of the Cantor-Bernstein-Schroeder theorem for general algebraic structures
negative_passages.docid: 155642
negative_passages.text: Understanding divison by monic polynomial in $R[x]$ where $R$ is an arbitrary ring
negative_passages.docid: 40014
negative_passages.text: A polynomial that is zero on an open set
negative_passages.docid: 128917
negative_passages.text: Inner Product on $\mathbb{R}$ and on $\mathbb{C}$
negative_passages.docid: 148813
negative_passages.text: Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.