Dyadic relations R and R’ are said to be similar (or ordinally similar) if there exists a one-one relation S whose domain is the field of R, and whose converse domain is the field of R’, such that, if aSa’ and bSb’ then aRb if and only if a’Rb’ . The relation-number of a dyadic relation may then be defined as the class of relations similar to it — cf. cardinal number.<\/p>\n
The relation-number of an ordering relation (see order) is called also an ordinal type or order type.<\/p>\n
The notion of a relation-number may be extended in a straightforward way to polyadic relations. — A.C.<\/p>\n
Whitehead and Russell, Principia Mathematica, vol. 2.<\/p>\n
Relation-number Dyadic relations R and R’ are said to be similar (or ordinally similar) if there exists a one-one relation S whose domain is the field of R, and whose converse domain is the field of R’, such that, if aSa’ and bSb’ then aRb if and only if a’Rb’ . The relation-number of a … Continue reading “Relation-number”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-79204","post","type-post","status-publish","format-standard","hentry","category-encyclopedic-dictionary"],"_links":{"self":[{"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/posts\/79204","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/comments?post=79204"}],"version-history":[{"count":0,"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/posts\/79204\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/media?parent=79204"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/categories?post=79204"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.biblia.work\/dictionaries\/wp-json\/wp\/v2\/tags?post=79204"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}