query: Is $C[0,1]$ larger than $\mathbb R$?
positive_passages.docid: 12003
positive_passages.text: Cardinality of set of real continuous functions
negative_passages.docid: 31544
negative_passages.text: How to prove that this polynomial is larger than another for positive reals?
negative_passages.docid: 74764
negative_passages.text: Dimension for a closed subspace of $C[0,1]$.
negative_passages.docid: 14516
negative_passages.text: The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
negative_passages.docid: 68490
negative_passages.text: For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
negative_passages.docid: 67851
negative_passages.text: Does $|x|^p$ with $0<p<1$ satisfy the triangle inequality on $\mathbb{R}$?
negative_passages.docid: 142174
negative_passages.text: Nonexistence of an injective $C^1$ map between $\mathbb R^2$ and $\mathbb R$
negative_passages.docid: 33642
negative_passages.text: Finite dimensional subspace of $C([0,1])$
negative_passages.docid: 138653
negative_passages.text: Is $\mathbb{R}$ a subspace of $\mathbb{R}^2$?
negative_passages.docid: 1162
negative_passages.text: Why $\{\mathbf{0}\}$ has dimension zero?
negative_passages.docid: 135511
negative_passages.text: $M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?
negative_passages.docid: 79285
negative_passages.text: Does there exist a continuous surjection from $\Bbb R^3-S^2$ to $\Bbb R^2-\{(0,0)\}$?
negative_passages.docid: 13765
negative_passages.text: Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
negative_passages.docid: 31990
negative_passages.text: Is $\{\frac{m}{10^n}\mid m,n\in\mathbb Z,\ n\geq 0\}$ dense in $\mathbb R$?
negative_passages.docid: 141799
negative_passages.text: Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
negative_passages.docid: 57967
negative_passages.text: Difference between $\mathbb C$ and $\mathbb R^2$
negative_passages.docid: 66272
negative_passages.text: Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?