The treatment of irrational numbers in the secondary schools
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The subject matter of this paper was suggested by the belief that a treatment of irrational numbers, from the stand point of the "cut" number, has certain points of superiority over the common treatment from the standpoint of limits. From the point of view of the high school and lower college courses, it is desirable to present a treatment of these topics at once as free as possible from all abstract and intricate logical considerations, and at the same time in harmony with a strictly logical treatment. It is desirable if possible that the student should have nothing to unlearn when he goes into higher work along these lines. It might be stated in passing that this has never practically been done by the limit process.