Pub Date : 2020-09-01DOI: 10.1007/978-1-319-16793-6_6
J. Rogawski, C. Adams
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A function from a set A to a set B is a map or a rule that assigns to each element in A an element in B. The rule can be expressed in words, as a picture, by a table of values or as by formula. Example 1. Let S be the set of all students in the Beginners group (who are in class today). Let C be the set of all chairs in the Beginners classroom. Define a function from the set of students S to the set of chairs C that assigns to each student the chair on which he or she is sitting. (a) Give two examples of elements of S. (b) Do we know the value of this function for every student? If not, give an example when the function is not defined.
{"title":"Functions on Sets","authors":"Beginners","doi":"10.2307/j.ctv14163vk.5","DOIUrl":"https://doi.org/10.2307/j.ctv14163vk.5","url":null,"abstract":"A function from a set A to a set B is a map or a rule that assigns to each element in A an element in B. The rule can be expressed in words, as a picture, by a table of values or as by formula. Example 1. Let S be the set of all students in the Beginners group (who are in class today). Let C be the set of all chairs in the Beginners classroom. Define a function from the set of students S to the set of chairs C that assigns to each student the chair on which he or she is sitting. (a) Give two examples of elements of S. (b) Do we know the value of this function for every student? If not, give an example when the function is not defined.","PeriodicalId":438476,"journal":{"name":"Honors Calculus","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131999927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Riemann integral is a fundamental part of calculus and an essential precursor to the Lebesgue integral. In this chapter we define the Riemann integral of a bounded function on an interval I = [a, b] on the real line.
{"title":"The Riemann Integral","authors":"","doi":"10.2307/j.ctv14163vk.11","DOIUrl":"https://doi.org/10.2307/j.ctv14163vk.11","url":null,"abstract":"The Riemann integral is a fundamental part of calculus and an essential precursor to the Lebesgue integral. In this chapter we define the Riemann integral of a bounded function on an interval I = [a, b] on the real line.","PeriodicalId":438476,"journal":{"name":"Honors Calculus","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129811527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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