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Teaching Undergraduate Mathematics on the Internet |
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| Authors: | |
| Institution: | (1) Department of Mathematics, Kent State University, Kent, OH 44242, USA;(2) Department of Mathematics, University of North Texas, Denton, Texas 76203, USA;(3) Department of Mathematics, Occidental College, Los Angeles, California 90041-3314, USA;(4) Department of Mathematical Sciences, Indiana University South Bend, South Bend, Indiana 46634, USA |
| Abstract: | This is Part 2 of a two-part study of how APOS theory may be used to provide cognitive explanations of how students and mathematicians might think about the concept of infinity. We discuss infinite processes, describe how the mental mechanisms of interiorization and encapsulation can be used to conceive of an infinite process as a completed totality, explain the relationship between infinite processes and the objects that may result from them, and apply our analyses to certain mathematical issues related to infinity. |
| Keywords: | APOS theory encapsulation history of mathematics human conceptions of the infinite infinite processes infinitesimals limit natural numbers |
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