# Homework Hints: Set-theoretic notation

Hi everyone,

I wanted to give an example of writing a given set in set-theoretic notation – this should help out with some of the problems on your first homework assignment (Section 1.1).

Example: Write in set-theoretic notation:  $\{5,10,15,20,\ldots \}$

In this case, you can see that the given set consists of all multiples of 5.  A good way to approach problems like this is to start with one of the basic sets, for example

•  the natural numbers $\mathbb{N} = \{1,2,3,4, \ldots \}$
• the integers $\mathbb{Z} = \{\ldots,-3,-2,-1,0,1,2,3,\ldots\}$

In this example, I can see that multiplying every natural number by 5 should give me the set that I want.  Therefore, I will use the formula $5n$, and the condition $n\in \mathbb{N}$.  Combining these in set-theoretic notation gives the solution:

Solution $\{ 5n : n\in \mathbb{N} \}$

Here are two ways to read this solution aloud:

• “the set of all $5n$ such that $n$ is a natural number”, or
• “for each $n$ in the natural numbers, multiply $n$ by $5$ and include the result in the set”

I hope this helps – feel free to respond here if you any questions.

Best,
Prof. Reitz

# Week 1 Assignments

Hi everyone,

Your first homework assignment will be exclusively in the book (you do NOT have a WeBWorK assignment this week), and is due on Tuesday.  Your first OpenLab Assignment is due on Thursday.

Welcome back,
Prof. Reitz

Week 1 Assignments
Written work  due Tuesday Sept 1st –  Sec 1.1 p.7: 1, 12, 19, 26, 29, 35
NOTE: On this assignment, odd problems are worth 2 points and even problems worth 4 points.
WeBWorK – none
OpenLab – Register for the OpenLab and join this course (instructions provided in a separate post).  “OpenLab #1: Advice from the Past” due Thurs Sept 3.

# OpenLab #1: Advice from the Past

Two years ago I taught this same course for the first time.   At the end of the semester, I gave my students the following assignment:

Imagine that you are invited to speak on the first day of MAT 2071, to give advice to entering students.  Write at least three sentences … describing what you would tell them.