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ERIC Number: EJ1108278
Record Type: Journal
Publication Date: 2016
Pages: 16
Abstractor: As Provided
ISSN: ISSN-0020-739X
Staircase and Fractional Part Functions
Amram, Meirav; Dagan, Miriam; Ioshpe, Michael; Satianov, Pavel
International Journal of Mathematical Education in Science and Technology, v47 n7 p1087-1102 2016
The staircase and fractional part functions are basic examples of real functions. They can be applied in several parts of mathematics, such as analysis, number theory, formulas for primes, and so on; in computer programming, the floor and ceiling functions are provided by a significant number of programming languages--they have some basic uses in various programming tasks. In this paper, we view the staircase and fractional part functions as a classical example of non-continuous real functions. We introduce some of their basic properties, present some interesting constructions concerning them, and explore some intriguing interpretations of such functions. Throughout the paper, we use these functions in order to explain basic concepts in a first calculus course, such as domain of definition, discontinuity, and oddness of functions. We also explain in detail how, after researching the properties of such functions, one can draw their graph; this is a crucial part in the process of understanding their nature. In the paper, we present some subjects that the first-year student in the exact sciences may not encounter. We try to clarify those subjects and show that such ideas are important in the understanding of non-continuous functions, as a part of studying analysis in general.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A