Hi everyone,

Our final exam will take place on Thursday, December 17th. The Review Sheet (and answer key) are posted under Classroom Resources/Exam Reviews. Please let me know if you find errors or have questions.

Regards,

Prof. Reitz

Hi everyone,

Our final exam will take place on Thursday, December 17th. The Review Sheet (and answer key) are posted under Classroom Resources/Exam Reviews. Please let me know if you find errors or have questions.

Regards,

Prof. Reitz

Hi everyone,

Your second exam will take place on Thursday, 10/22. The review sheet is posted on the OpenLab (under Classroom Resources/Exam Reviews). The answer key comes after the questions in the document – please let me know by email or here on the OpenLab if you discover an error or have a question.

Good luck with your studies,

Prof. Reitz

Hi everyone,

This is a followup to Thursday’s lecture, and should provide a little help with some of the homework problems (I’m looking at you, Problem 7).

**Example.** Consider the intervals of real number and . Find their intersection and their union .

One key idea is that these are intervals of the real numbers, so they include not just the whole numbers but *all* numbers between the endpoints. The set includes all numbers that are great than or equal to 2 and less than 5. This means that includes 2, 3 and 4, but also decimals such as 3.5 or 4.9998. The set includes all numbers greater than 4, such as 4.1 or six billion.

The intersection will be the places where these two overlap – it will include numbers greater than 4 but less than 5 (NOTE: it does *not* include the numbers 4 and 5 themselves, but it does include, for example, 4.3). In interval notation, we write:

The union will include all numbers greater than or equal to 2, written:

**WeBWorK Tip:** To enter the infinity symbol, just use the word “infinity” like this:

[2, infinity)

**WeBWorK Tip:** Sometimes in WeBWorK, your answer will consist of two different intervals – you want to include them both in the answer. To do this, connect them with a union symbol (just use the capital U on your keyboard). Here is a (made up) example:

Not sure if these will help, but they may give you a little more to go on – feel free to leave a comment here or send me an email if you have questions.

Best of luck!

Prof. Reitz

WeBWorK is accessible from on and off campus (anywhere you have access to the internet). Your first two WeBWorK assignments are due on Tuesday, September 9th, at midnight, and will cover the material from the first two weeks of class (primarily from the second week). Here’s what you have to do:

**Assignment. **To get started , you must complete the following three steps.

**Step 1. ***Log in to WeBWorK* here: http://mathww.citytech.cuny.edu/webwork2/MAT2071-F15-Reitz/. I have created Usernames and Passwords for each student registered for my class.

**Username. **Your username for WeBWorK consists of your first initial plus your last name, all lowercase (for example, John Smith would have username ‘jsmith’).

**Password. **Your temporary password is the same as your username (if your username is ‘jsmith’, your password is currently ‘jsmith’).

**Step 2. ***Change your password and update your email address*. To do this, select “Password/Email” from the main menu on the left. Use whatever email address you like (I suggest using one that you check often).

**Step 3. ***Complete the first two assignments*, titled **Assignment1-Sec1.2-1.3** and **Assignment2-Sec1.4-1.7.** Click on an assignment on the main screen to get started.

If you have any trouble – either with logging in, or with completing the assignment, post a comment here or send me an email and I will get back to you.

**WeBWorK Tips:**

- Click on a problem to see the details (the list of problems appears in the menu on the left). Enter an answer and hit “Submit Answers”. Don’t worry, if you get it wrong you can try it again.
- You can work on the problems in any order you wish. You can do some problems now, and come back and do the rest another day (your work will be saved, as long as you submit your answers).
- If you want to print out a copy of the assignment, click on the assignment name in the main menu on the left, and then click the link in the main screen area that reads “Download a hardcopy of this homework set.”

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:

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
- the integers

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 , and the condition . Combining these in set-theoretic notation gives the solution:

**Solution**

Here are two ways to read this solution aloud:

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

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

Best,

Prof. Reitz

This course is MAT 2071, Introduction to Proofs and Logic, taking place in the Fall 2015 semester with Professor Reitz. We will be using this website in a variety of ways this semester – as a central location for information about the course (assignments, review sheets, policies, and so on), a place to write about the work we are doing, to ask and answer questions, to post examples of our work, and to talk about logic, proofs, mathematics, reality and so on.

**Getting Started**

Anyone on the internet can look around the site and see what we are doing, and even leave a comment on one of the pages. However, only registered users can create new posts and participate in the discussion boards.

**How do I register?**

You will need to do two things:

- If you have not used the OpenLab before, you must first create an account. You will need access to your citytech email address for this. Detailed instructions for signing up on the OpenLab can be found here.
- Once you have created an account on the OpenLab,
**log in and then join this particular course**, 2015 Fall – MAT 2071 Proofs and Logic – Reitz. To do this, first click the “Course Profile” link at the top left of this page (just under the picture). Then click the “Join Now” button, which should appear just underneath the picture.

**Problems with the OpenLab or with your CityTech email:**

Please let me know if you run into any problems registering or joining our course (send me an email, jreitz@citytech.cuny.edu). I also wanted to give you two resources to help out in the process:

1. For problems with your **citytech email account**, contact the **Student Computing Helpdesk**, either in person, by phone, or by email:

**Student Computing Helpdesk
**Location: Namm First Floor – Information Booth

Hours: TBD (usually 9am – 5pm Mon-Fri)

Phone: 718.260.4900

E-mail: Studenthelpdesk@citytech.cuny.edu

Their website also contains tutorials and FAQ on common problems

2. For problems **registering for the OpenLab**, contact the **OpenLab support team**, either by email at openlab@citytech.cuny.edu, or by following this link.