---
tags: mth225, dailyprep
---

# Daily Prep 3.1 -- MTH 225

## Overview

Welcome to Module 3! In this module we'll be learning all about another fundamental concept in mathematics and in computer science: the **set**, which is the foundation for all data structures and a basic tool for expressing collections of objects. In this lesson we'll learn what a set is, the differences between a *finite* and an *infinite* set, what it means to be an *element* of a set, and some famous sets we'll use repeatedly. The main focus of our class work will be on mastering the two different ways of expressing a set: *roster notation* and *set-builder notation*.

## Learning objectives

**Basic Learning Objectives:** *Before* our class meeting, use the Resources listed below to learn all of the following. You should be reasonably fluent with all of these tasks prior to our meeting; we will field questions on these, but they will not be retaught.

- Determine whether a set is finite or infinite.
- Given a set in roster notation and given an object, determine whether the object is an element of the set and express the outcome using the $\in$ or $\not \in$ symbol.
- Identify "famous" sets corresponding to their notation: The empty set, the natural numbers, and the real numbers.

**Advanced Learning Objectives:** *During and after* our class meeting, we will work on learning the following. Fluency with these is not required prior to class.

- Given a set in roster form, rephrase the set in set-builder notation; and vice versa.
- Given a set in either roster or set-builder form and an object, determine whether the object is a member of the set.

## Resources for learning

**Video:** Watch these from [the MTH 225 playlist](https://vimeo.com/showcase/8667148) (total running time 19:50):

<iframe src="https://player.vimeo.com/video/602725171?h=c1ad889571" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen></iframe>
<p><a href="https://vimeo.com/602725171">Screencast 3.1: Sets</a> from <a href="https://vimeo.com/user132700952">Robert Talbert</a> on <a href="https://vimeo.com">Vimeo</a>.</p>

<iframe src="https://player.vimeo.com/video/602744516?h=37e17ab6d5" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen></iframe>
<p><a href="https://vimeo.com/602744516">Screencast 3.2: Roster and set-builder notation</a> from <a href="https://vimeo.com/user132700952">Robert Talbert</a> on <a href="https://vimeo.com">Vimeo</a>.</p>

<iframe src="https://player.vimeo.com/video/602761420?h=f2ce3b063f" width="640" height="360" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" allowfullscreen></iframe>
<p><a href="https://vimeo.com/602761420">Screencast 3.3: When is an object an element of a set?</a> from <a href="https://vimeo.com/user132700952">Robert Talbert</a> on <a href="https://vimeo.com">Vimeo</a>.</p>

**Text:** Read in the textbook, [Section 0.3](http://discrete.openmathbooks.org/dmoi3/sec_intro-sets.html) through Example 0.3.2.

You are free to search for and use other resources in addition to, or instead of the above, as long as you can work the exercises below.

## Exercises

Once you have watched the videos above, go to this form and complete all the non-optional items on it:

https://docs.google.com/forms/d/e/1FAIpQLSdShs66LpjTaMkyfSoXu9fxn38Zn5ZQRQ-ifdW80WrMRLrjfQ/viewform

## Submission and grading

**Submitting your work:** Your work is submitted when you submit the Google Form. You should receive an email receipt indicating that the work was submitted successfully.

**How this is graded:** The pre-class portion of the Daily Prep is graded either 0 points or 1 point, on the basis of completeness and effort. Wrong answers are not penalized. Earning a "1" requires that you:

- Turn the work in before its deadline;
- Leave no item blank or skipped, even accidentally; and
- Give a good-faith effort at a correct answer on every non-optional item.

More information can be found in the [Specifications for Satisfactory Work in MTH 225](/Cy6P0rGZQzuOM3NwZ3ZuMw) document.

When you arrive for the class meeting, you'll be put into a group of 2-3 to complete a quiz over this material, which will be graded on a 0/1 scale on the basis of correctness.