Math 360, Fall 2013, Assignment 1
From cartan.math.umb.edu
The beginner ... should not be discouraged if ... he finds that he does not have the prerequisites for reading the prerequisites.
- - P. Halmos
Carefully define the following terms, then give one example and one non-example of each:
- Cartesian product (of two sets).
- Relation (on a set \(A\)).
- Reflexive relation.
- Symmetric relation.
- Transitive relation.
- Equivalence relation.
- Partition (of a set).
- Cell (of a partition).
Solve the following problems:
- Section 0, problems 1, 5, 7, and 11.
Questions:
1.) As a confirmation, because I don't have a hard copy of the book yet, the questions are:
- 1.) Describe the following set by listing it's elements\[\{x\in\mathbb{R} | x^2=3\}\]
- For 5 and 7, decide whether the object described is a set (is well defined). Give an alternative description of each set.
- 5.) \(\{n\in\mathbb{Z}^+ | n \ is \ a \ large\ number\}\)
- 7.) \(\{n\in\mathbb{Z} | 39 < n^3 < 57\} \)
- 5.) \(\{n\in\mathbb{Z}^+ | n \ is \ a \ large\ number\}\)
- 11.) List the elements in \(\{a,b,c\} x \{1,2,c\}\)
Thank you for your help in advance. --Robert.Moray (talk) 19:06, 6 September 2013 (EDT)
Yes, those are correct.
