query: show that there's a linear ordering such that $R \subseteq R^*$
positive_passages.docid: 76521
positive_passages.text: Every partial order can be extended to a linear ordering
negative_passages.docid: 77493
negative_passages.text: Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
negative_passages.docid: 59133
negative_passages.text: Show that an inverse of a bijective linear map is a linear map.
negative_passages.docid: 15966
negative_passages.text: A way to well-order real line
negative_passages.docid: 80279
negative_passages.text: Show that $S + T$ and $aT$ are linear
negative_passages.docid: 112231
negative_passages.text: Showing that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set
negative_passages.docid: 127687
negative_passages.text: Proof of the duality of the dominance order on partitions
negative_passages.docid: 21568
negative_passages.text: Maximal order of an element in a symmetric group
negative_passages.docid: 6478
negative_passages.text: Prove that for any infinite poset there is an infinite subset which is either linearly ordered or antichain.
negative_passages.docid: 5089
negative_passages.text: An element of a group has the same order as its inverse
negative_passages.docid: 86926
negative_passages.text: Why isn't this a well ordering of $\{A\subseteq\mathbb N\mid A\text{ is infinite}\}$?
negative_passages.docid: 72391
negative_passages.text: linear dependence proof using subsets
negative_passages.docid: 98734
negative_passages.text: Order of a product of elements in a generic group
negative_passages.docid: 2575
negative_passages.text: Showing that $\mathbb{R}$ is connected
negative_passages.docid: 62977
negative_passages.text: Show on $\mathbb{N}$ there are $2^{\aleph_0}$ nonisomorphic linear orders.
negative_passages.docid: 104034
negative_passages.text: Is $\le$ defined by $\langle 𝑥_1, 𝑦_1 \rangle \le \langle 𝑥_2, 𝑦_2 \rangle$, if $𝑥_1 \le 𝑥_2 \land𝑦_1 \ge 𝑦_2$ a linear order?
negative_passages.docid: 146421
negative_passages.text: How to prove a total order has a unique minimal element