# Ordinals Sentence Examples

Similarly, a class of serial relations, called well-ordered serial relations, can be defined, such that their corresponding relation-numbers include the ordinary finite

**ordinals**, but also include relation-numbers which have many properties like those of the finite**ordinals**, though the fields of the relations belonging to them are not finite.This is almost always true of proofs that use countable

**ordinals**.Now comes the moment to admit that my ` applications ' of countable

**ordinals**were, in a sense, a con.Additional time

**ordinals**can also be expressed using numbers.For example, Lisu has up to three preceding and six following day

**ordinals**, also three preceding and three following year**ordinals**.Owing to the correspondence between the finite cardinals and the finite

**ordinals**, the propositions of cardinal arithmetic and ordinal arithmetic correspond point by point.The arithmetic of the infinite cardinals does not correspond to that of the infinite

**ordinals**.It will suffice to mention here that Peano's fourth premiss of arithmetic does not hold for infinite cardinals or for infinite

**ordinals**.Our ability to think about transfinite

**ordinals**is one of the things to be explained.The definitions of the finite

**ordinals**can be expressed without use of the corresponding cardinals, so there is no essential priority of cardinals to**ordinals**.AdvertisementHere also it can be seen that the science of the finite

**ordinals**is a particular subdivision of the general theory of classes and relations.Contrasting the above definitions of number, cardinal and

**ordinals**, with the alternative theory that number is an ultimate idea incapable of definition, we notice that our procedure exacts a greater attention, combined with a smaller credulity; for every idea, assumed as ultimate, demands a separate act of faith.In the case of lists and schedules the numbers are only

**ordinals**; but in the case of mathematical or statistical tables they are usually regarded as cardinals,though, when they represent values of a continuous quantity, they must be regarded as**ordinals**(§§ 26, 93).Thus (writing

**ordinals**in light type, and cardinals in heavy type) 9 comes after 4, and therefore 9 is greater than 4.