Ordinals sentence example
- 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.Advertisement
- 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.Advertisement
- Here 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.