{"id":{"repo_id":"wku-diss","oai_identifier":"oai:digitalcommons.wku.edu:theses-1243"},"canonical_url":"https://search.dev.ndltd.org/etd/wku-diss/oai:digitalcommons.wku.edu:theses-1243","repository":{"repo_id":"wku-diss","name":"Western Kentucky University","base_url":"https://digitalcommons.wku.edu/do/oai/"},"display":{"title":"Continued Radicals","abstract":"If a1, a2, . . . , an are nonnegative real numbers and fj(x) = paj + x, then f1o f2o· · · fn(0) is a nested radical with terms a1, . . . , an. If it exists, the limit as n ! 1 of such an expression is a continued radical. We consider the set of real numbers S(M) representable as an infinite nested radical whose terms a1, a2, . . . are all from a finite set M. We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the Cantor set.","abstract_html":"If a1, a2, . . . , an are nonnegative real numbers and fj(x) = paj + x, then f1o f2o· · · fn(0) is a nested radical with terms a1, . . . , an. If it exists, the limit as n ! 1 of such an expression is a continued radical. We consider the set of real numbers S(M) representable as an infinite nested radical whose terms a1, a2, . . . are all from a finite set M. We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the Cantor set.","abstract_has_math":false,"creators":["Johnson, Jamie"],"institution":null,"degree_name":"Master of Science","degree_level":null,"degree_discipline":"Department of Mathematics and Computer Science","degree_department":null,"school":null,"contributors":["Dr. Tom Richmond (Director), Dr. John Spraker, Dr. Daniel C. Biles"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2005,"date_issued":"2005-01-01T08:00:00Z","date_published":"2005-01-01T08:00:00Z","updated_at":"2026-07-24T06:07:16Z","subjects":["Radical Numbers","Mathematics","Geometry and Topology"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.wku.edu/theses/240","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. Tom Richmond (Director), Dr. John Spraker, Dr. Daniel C. Biles"]},{"key":"dc:creator","label":"Author","values":["Johnson, Jamie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematics and Computer Science"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Radical Numbers","Mathematics","Geometry and Topology"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.wku.edu/theses/240"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["If a1, a2, . . . , an are nonnegative real numbers and fj(x) = paj + x, then f1o f2o· · · fn(0) is a nested radical with terms a1, . . . , an. If it exists, the limit as n ! 1 of such an expression is a continued radical. We consider the set of real numbers S(M) representable as an infinite nested radical whose terms a1, a2, . . . are all from a finite set M. We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the Cantor set."]},{"key":"dc:title","label":"Title","values":["Continued Radicals"]}]}],"canonical_facts":{"dc:contributor":["Dr. Tom Richmond (Director), Dr. John Spraker, Dr. Daniel C. Biles"],"dc:creator":["Johnson, Jamie"],"dc:description.abstract":["If a1, a2, . . . , an are nonnegative real numbers and fj(x) = paj + x, then f1o f2o· · · fn(0) is a nested radical with terms a1, . . . , an. If it exists, the limit as n ! 1 of such an expression is a continued radical. We consider the set of real numbers S(M) representable as an infinite nested radical whose terms a1, a2, . . . are all from a finite set M. We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the Cantor set."],"dc:identifier":["https://digitalcommons.wku.edu/theses/240"],"dc:subject":["Radical Numbers","Mathematics","Geometry and Topology"],"dc:title":["Continued Radicals"],"dc:type":["Thesis"],"thesis:degree_discipline":["Department of Mathematics and Computer Science"],"thesis:degree_name":["Master of Science"]},"updated_at":"2026-07-24T06:07:16Z"}