TY - JOUR

T1 - Finite and infinite sets

T2 - Definitions and intuitions

AU - Tirosh, D.

PY - 1999

Y1 - 1999

N2 - The study explores the intuitive methods different-aged students use to determine whether a given set is finite or infinite; it also examines the relationship between these methods and the accepted, mathematical definition of infinite sets. It was found that two main methods were intuitively used by students: examining the finite/infinite nature of a process involving the elements of a given set, and comparing the given set with another, seemingly ‘richer’ set. The intuitive use of each of these methods largely departed from the formal one. In the concluding part it is argued that the inner contradictions in students' intuitive grasp of infinite sets could be used to increase their awareness of the fundamental role of definitions in mathematics.

AB - The study explores the intuitive methods different-aged students use to determine whether a given set is finite or infinite; it also examines the relationship between these methods and the accepted, mathematical definition of infinite sets. It was found that two main methods were intuitively used by students: examining the finite/infinite nature of a process involving the elements of a given set, and comparing the given set with another, seemingly ‘richer’ set. The intuitive use of each of these methods largely departed from the formal one. In the concluding part it is argued that the inner contradictions in students' intuitive grasp of infinite sets could be used to increase their awareness of the fundamental role of definitions in mathematics.

UR - http://www.scopus.com/inward/record.url?scp=21244438070&partnerID=8YFLogxK

U2 - 10.1080/002073999287879

DO - 10.1080/002073999287879

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AN - SCOPUS:21244438070

SN - 0020-739X

VL - 30

SP - 341

EP - 349

JO - International Journal of Mathematical Education in Science and Technology

JF - International Journal of Mathematical Education in Science and Technology

IS - 3

ER -