Letter to the Editor

doi:10.5951/mt.62.8.0694

Letter to the Editor

Mathematics Teacher ◽

10.5951/mt.62.8.0694 ◽

1969 ◽

Vol 62 (8) ◽

pp. 694

Keyword(s):

Mathematics Teacher ◽

Binary Operation ◽

Algebraic Operation ◽

Letter To The Editor

Concerning the illustration of the commutative and the associative properties described by James Bilderback in his letter in The Mathematics Teacher, LXI (February, 1968), 122-35—“holding hands” is not a binary operation in the algebraic sense, since it does not associate a unique third student with each ordered pair of students. It appears to me that Mr. Bilderback's method will not only fail to achieve the desired result but it may tend to reinforce the misconception of an algebraic operation as a configuration of marks on the paper rather than as a mapping from S × S V S where S is the set of elements under consideration.

Download Full-text

Instant Insanity: That Ubiquitous Baffler

Mathematics Teacher ◽

10.5951/mt.65.2.0131 ◽

1972 ◽

Vol 65 (2) ◽

pp. 131-135

Author(s):

Dewey C. Duncan

Keyword(s):

Mathematics Teacher ◽

The Other ◽

Letter To The Editor

This discussion is occasioned by two notes in the October 1969 issue of the Mathematics Teacher, one a letter to the editor from Barbara Almli on page 446, and the other Philip Peak's review on page 477 in his “Have You Read …?” section of T. A. Brown's “A Note on ‘Instant Insanity’” (Mathematics Magazine, September 1968, pp. 167-69). Each of these items describes the puzzling challenge known as “Instant Insanity.”

Download Full-text

Letter to the Editor

Mathematics Teacher ◽

10.5951/mt.61.7.0701 ◽

1968 ◽

Vol 61 (7) ◽

pp. 701-712

Author(s):

C. F. Hockett ◽

Vida Augulis

Keyword(s):

Mathematics Teacher ◽

Hausdorff Space ◽

Considerable Importance ◽

Interesting Article ◽

Letter To The Editor

In his interesting article in The Mathematics Teacher in the April 1968 issue, pages 304-95, Earl K McGeehee, Jr., fails to mention one nomenclatural point of considerable importance: A Hausdorff space that is also a door space is a house door space.

Download Full-text

Letters to the Editor

Mathematics Teacher ◽

10.5951/mt.61.3.0245 ◽

1968 ◽

Vol 61 (3) ◽

pp. 245-327

Keyword(s):

Mathematics Teacher ◽

Letters To The Editor ◽

Letter To The Editor

I note with interest the letter to the editor written by Duane Forsyth in the October 1967 issue of THE MATHEMATICS TEACHER, page 640, concerning a symbol for the inverse of a number.

Download Full-text

Effect Algebras of Positive Self-adjoint Operators Densely Defined on Hilbert Spaces

Acta Polytechnica ◽

10.14311/1412 ◽

2011 ◽

Vol 51 (4) ◽

Author(s):

Z. Riečanová

Keyword(s):

Hilbert Spaces ◽

Binary Operation ◽

Complex Hilbert Space ◽

Linear Operators ◽

Algebraic Operation ◽

Effect Algebras ◽

Infinite Dimensional ◽

Adjoint Operators ◽

Densely Defined ◽

Generalized Effect Algebras

We show that (generalized) effect algebras may be suitable very simple and natural algebraic structures for sets of (unbounded) positive self-adjoint linear operators densely defined on an infinite-dimensional complex Hilbert space. In these cases the effect algebraic operation, as a total or partially defined binary operation, coincides with the usual addition of operators in Hilbert spaces.

Download Full-text