After using his 1878 definition, Cantor stated that in an 1883 article he proved that cardinalities are well-ordered, which implies they are linearly ordered.
22.
A graph is strongly chordal if and only if every one of its induced subgraphs has a simple vertex, a vertex whose neighbors have neighborhoods that are linearly ordered by inclusion.
23.
Since a linear order induces a cyclic order, cyclically ordered groups are also a generalization of linearly ordered groups : the rational numbers, the real numbers, and so on.
24.
In other words, a cyclically ordered set can be thought of as a locally linearly ordered space : an object like a manifold, but with order relations instead of coordinate charts.
25.
"' Unsigned Lah numbers "'have an interesting meaning in combinatorics : they count the number of ways a partitioned into " k " nonempty linearly ordered subsets.
26.
By analogy with an Archimedean linearly ordered group, one can define an Archimedean cyclically ordered group as a group that does not contain any pair of elements such that for every positive integer.
27.
Consider a finite set that is linearly ordered, or ( equivalently, for purposes of this definition ) arranged in a cyclic order like the vertices of a regular " n "-gon.
28.
Beyond the problem of defining set representatives for ordinal numbers, Scott's trick can be used to obtain representatives for cardinal numbers and more generally for linearly ordered sets ( Jech 2003 : 65 ).
29.
In classical logic, quantifier prefixes are linearly ordered such that the value of a variable " y m " bound by a quantifier " Q m " depends on the value of the variables
30.
A space whose topology is an order topology is called a Linearly Ordered Topological Space ( LOTS ), and a subspace of a linearly ordered topological space is called a Generalized Ordered Space ( GO-space ).
