Math 3334: Class Notes

Definition 1 – The statement that P is a point means P is an ordered number pair.

Defintion 2 – The statement that Q is the plane means Q is the set of all points.

Definition 3 – Suppose each of x and y is a point. The statement that D is the distance between x and y means D= [(x1– y1)2 + (x2-y2)2]1/2 where X=(x1, x2) and Y=(y1, y2).

Definition 4 – The statement that R is a region means there is a positive number c and a point P and R is the set to which x belongs, only in the case x is a point and D(x,p) < c. We may denote such a region by Rc(P).

Problem 1 – if each of R and S isa region adn there is a point P common to R and S, then tehre is a region T such taht P is in T and every point of T is in each of R and S.

Definition 5 – Suppose M is a point collection. The statement that P is a limit point of M means P is a point and if R is a region containing P, then tehre is apoint of M, distance from P, that belongs to R.

Problem 2 – Every point of a region R is a limit point of the region R.

Problem 3 – If R is a region and P is a point not in R, then P is not a limit point of R.

Problem 4 – If M is a number collection that contains the number 1 and if n belongs to M, then n+1 belongs to M, does M contain all positive integers?

Definition 6 – The statement that M is an infitie point collection means if N is a positive integer then M has N points.

Morning at the Houston Zoo

My wife found out about a month ago that we were members of the Houston Zoo.  We have been members off and on for the past five years, so her suprise was a suprise to me :-)  Anyway, now she wants to maximize her value.  So, she wants to go every Saturday. 

 Here in Houston in the summer, it gets very hot very quickly.  So, her idea has been to get there at opening time and to stay an hour or two.  Last Saturday we got there at 9:30, which is 30 minutes past the opening time.  This saturday, we got up early and tried to leave the house at 8, but ending up leaving closer to 8:30.  We get there right at 9:15 and a guy at the gate tells us about “Member Mornings”.  The zoo has a special session with a zookeeper every second saturday just for members.  Today it was for the specticaled bears.  We got to watch them eat and get let out of their cages to the display.  We also got to talk to the zoo keeper.

We also saw an African Crowned Crane.  We saw one of these at the Animal Kingdom Lodge during our summer vacation.  We saw the elephants, warthog, meerkats, and several other animals.  At about 10:30, they were tired of looking at animals and it had gotten very hot so we left.

Went to the UH library to return some books.  Went to WalMart to pick up two T-shirts for the children since they had decided to pour the water bottles on themselves in the car to cool off.  They were soaking wet, and we wanted to eat.  Then off to Lubby’s.  My youngest son saw fried okra and thought it was chicken nuggets.  He was convinced they had chicken nuggets and said that was all he wanted.  So, I asked them if they had chicken nuggets, and they said they could make it.  I never realized that Lubby’s had some “by request” items.  I thought you only could get what was on the servering line.

Now we are all at home, trying to rest up this evenings events.


WebSite: World eBook Library

From the website:

“World’s largest eBook Consortia
Housed in World eBook Library Multi-Terabyte server network is the world’s largest digital archive of PDF eBooks and eDocuments. Our collection hosts more than 330,000+ PDF eBooks and eDocuments. As a member you will have complete access to the entire collection. Our collection is constantly growing. Our projection is to reach 500,000 by fall of 2007.”

Only $8.95 per year!  It seems to be worth it.  Do any of you use this service?  Leave a comment on how you like it.

WebSite: World Of Inspiration

You should check out the World Of Inspiration website:

Here are some quotes from their homepage:

“There are two types of people who will tell you that you cannot make a difference in this world: Those who are afraid to try and those who are afraid you will succeed.”

Ray Goforth

“Many of us spend half our time wishing for things we could have if we didn’t spend half our time wishing.”


“Success is not to be measured by the position someone has reached in life, but the obstacles he has overcome while trying to succeed.”

Booker T. Washington

Rocketboom: Breakdancing

Today’s rocket boom is worth watching.

Today’s episode shows a break dancing event in NYC.  It is just amazing what some people can do with their bodies.  Anyway, it is worth a look.

JOKE: Manager and two workers go out to eat

I heard this joke at Toastmasters yesterday.  I thought it was pretty funny and that you might enjoy it as well.

A Manager and two workers go out to lunch.  At lunch they see this old lamp on their table.  They begin to rub it and sure enough a genie comes out.  The genie says, “Normally I would give you three wishes.  But since there are three of you, I will give each of you one wish.”

Worker 1 says, “Let me go first.”

The Genie says, “What is your wish?”

Worker1: “I want to go to Florida, be on the beach all day, and not have to worry about anything.”

And just like that, it was done.

Worker 2 says, “Let me go next”

The Genie says, “What is your wish?”

Worker 2 says, “I would like to Hawaii and surf all day.”

And just like that, it was done.

Next it was the Manager’s turn, and the Genie says, “What is your wish?”

The manager says, “I want those two workers back here right now so they can finish their jobs!”

Moral of the story: “Let your manager go first!”

Bush: “Is that Sam Donaldson?”

I like reading the quotes in the U.S. News & World Reports. You find people saying all sorts of interesting things. In the August 14-21, 2006 edition, we have the following Bush quote:

“Is that Sam Donaldson? Forget it. You’re a has-been. We don’t have to answer has-beens’ questions.”

The caption under it says, “President Bush, at a ceremony to close the old pressroom for renovation during which past media and White House press personalities like Donaldson, who shouted a question, appeared.”

My first thought was, “What was the question?”

The question appears to have been, “Should Mel Gibson be forgiven for claiming that the Jews start all the wars?” (Source: The Raw Story and YouTube)

My second thought was, “How could a President treat such a distinguished reporter that way? And he may not have to answer ‘has-beens” questions, but he need to answer Citizens’ questions, and Sam is a citizen.”

Well, thanks to the power of the Internet, I was able to see a live video recording of the event on YouTube The entire event was a funny event with the President calling himself a “Crackpot from Texas”. Based upon the video, everything was said in jest.  I do not even think that Sam was asking a serious question but rather just going along with the mood.  Yet, that is not what was communicated by the U.S. News & World Report blurb.