To have the same order type is an equivalence relation on the class of well-ordered sets, and the ordinal numbers are the equivalence classes.
42.
Taking the coefficients to be the rational functions in a different variable, say " y ", produces an example with a different order type.
43.
Expertise traits are unlocks that accentuate their given line-new ammo types for Engineers, more order types for Officers, and different damaging effects for Vanguards.
44.
The cofinality of an ordinal \ alpha is the smallest ordinal \ delta that is the order type of a cofinal subset of \ alpha.
45.
Law-and-order types decried the state's inability to pass a new death penalty law, even though all the state's top leaders said they supported the idea.
46.
"Prosecutors, especially in a death penalty case, want strong law-and-order types, " said Jeffrey Abramson, a professor of politics and legal studies at Brandeis University.
47.
Thus, the moaning of moralists, the hand-wringing of law-and-order types and the unhappiness of culturecampers at the artful Clinton's latest dodge are at least premature.
48.
For an infinite set the order type determines the cardinality, but not conversely : well-ordered sets of a particular cardinality can have many different order types.
49.
For an infinite set the order type determines the cardinality, but not conversely : well-ordered sets of a particular cardinality can have many different order types.
50.
Mathematicians more typically choose to ground notions of number in set theory, for example they might model natural numbers by the order types of finite well-ordered sets.
