A Well Ordering Principle
In set theory, we describe a set as being totally ordered if there exists a binary relation, , that is antisymmetric, transitive and total.
- A binary relation, is antisymmetric if and
- A binary relation, is transitive if and
- A binary relation, is total if either or for every
Now, a totally ordered set is said to be well-ordered if every subset has a least element, that is, . In other words, if a set has the property that every subset, or part, of it will have a least element. For example, the set of positive integers, is well-ordered since no matter which group of those numbers you pick, there will be a smallest one. On the other hand, the set of all integers, is not well-ordered since you could take a subset that contains all the numbers down to negative infinity and thus, has no least element.
By now, I have probably lost all of my current readers so let me get to my point. As I was pondering this concepted of well-ordered sets, I recognized a something applicable outside of the world of mathematics. In today's world, we are told to leave our work at the office, to leave our family life at home and to keep our faith to ourselves, all so as to not offend anyone. So, we compartmentalize. We put each part of our life separate from the other. Now there is something to be said for this but clearly the faith that we have cannot be kept separate from the rest of our life.
So I propose a new definition. Let us say that a well-ordered LIFE is one in which every part of our life has a "least element." And by "least element", I am thinking in terms of a foundational element or a most important element or maybe even a guiding element.
This definition brings new light to the often quoted passage, "Seek first the kingdom of God." When Jesus said this, he could have meant that we are to put Him first, chronologically. The first thing we are to do each morning is seek the kingdom. When Jesus said this, he could have meant that we are to put Him first, by importance. For example, any time there is a scheduling conflict between church and family, work or play, we must put the church first. Now, certainly our life is better off through prioritizing our faith, and yet, doesn't Jesus mean more than either of these. The principle of seeking first the kingdom is summarized well by the well-ordering principle. Every area of our life should be built on our faith, informed by our faith, permeated by our faith and inseparable from our faith. That is putting the kingdom first and that is a principle I need to work on.
Do you have a well-ordered life?
How many times can you watch "Finding Nemo" before you lose your mind? I don't know for sure but I know that 5 times in as many days must be close. This entry's title is one of my most quoted lines of the film (as the flounder hunts for those hooligans playing in his yard). ANYWAYS, to those that are asking that of the yours truly, I must say that my best days of blogging are yet to come. So far, I have blogged sporadically at best. I'd like to make this a decent resource for students and math enthusiasts to come and stretch their mind. (Yes, there is such a thing as a math enthusiast, and if you are not one, be careful: I'm out to convert you). So far, I don't think I am succeeding.
I have a couple of ideas as a theme for this blog (in addition to personal blogging of my life's work):
1. Mathematical illustrations of spiritual principles.
Consider the fact that science is man's study of God's creation. The language of science is mathematics. So its clear, the language of the Creator isn't Hebrew but mathematics. Maybe that's stretching it a bit, but there are a great many methods of mathematical analysis that can be used to illustrate spiritual principles.
2. Favorite theorem of the week.
Most mathematical theorems are marvels in logical thought and can be proved in amazing eloquent arguments. Mathematics can be absolutely beautiful, so its a great opportunity to describe those items I love about it.
3. Mathematical application of the week.
Mathematics is all around us. We can use it to solve all kinds of problems that come up everyday. Students often ask, "where will I ever have to use this?" I tell them all the same thing. Nowhere!! Its not a matter of "have to" but of "able to." Those who choose to use what they've learned are more employable, promotable and just plain interesting.
Any preference or other ideas?
I guess there are worse mistakes I could make than on the previous post. This is an answer given to a quiz in a general math course (not one of mine):
(HT: jonboy, thanks for the email)
So, the rest of my day is now shot. For the rest of the day, I will do nothing but think about a mistake I made this morning. Here's the story:
Background: I love it when people come to me with questions, especially if it is from someone besides my students, like a friend in town or maybe even a complete stranger with a math question. I don't get many of these calls, but when I do, I am very pleased to help.
This morning a man in my church called and said that he had a math question for me. There is a butcher in town that has 30 lbs of beef trat is 93% lean and wants to add fat to make it 90% lean. How much fat should he add. He was also kind enough to tell me that he had already called the Division chair in the Business department to get an anwer. I was witty enough reply, "So you want to double check his answer?" To which he replied, "Or yours." At that moment in the conversation, a person came into my office so I had to call this man back.
As soon as I was done, I made the following calculations:
Let be the amount of fat to be added. Then, 30 lbs of fat at 93% lean means there is 93% lean beef, or 27.9 lbs, and 7% fat, or 2.1 lbs. Thus we need 10% of to be . So we have:
[Unparseable or potentially dangerous latex formula. Error 5 : 657x53]
So the answer is clearly lbs. of fat. WRONG. Only I discover that I am wrong after I've called him back. The correct answer, which by the way, the Business Prof. was able to get is 1 lb. fat. Clearly on line two above, if you subtrack 2.1 from 3.0 you do NOT get 1.8 but 0.9. Dadgummit! Am I dyslexic or what? I don't how I let that get by and now I have demonstrated incompetence in a simple area of algebra. ARGH!
What a day!
This past Sunday, I had the opportunity to fill in at First Baptist Church, Muleshoe, TX. Both the pastor, Dr. Stacy Conners, and the music minister had left town to go to the state convention in Austin. Dr. Sadler, of the religion department at Wayland, had been contacted by the church and he gave them my name. It has been a long time since I had the chance to go and preach somewhere, so I was a little nervous. But overall, the morning went very well. I was a little shaky on the ending of my sermon mainly from nerves. I was asked just before the service to be completely in charge of the invitation and I've not done that before.
The biggest surprise of the morning came as the music leader was inviting everyone to come back that evening and hear Dr. Franklin again. Again??? Nobody told me about being needed for Sunday night! So, I got to spend the afternoon preparing another sermon. But this entry is about the morning service, so I'll give you the Sunday night sermon in the next blog entry.
Below is the sermon I preached in Muleshoe on Sunday morning. It is in mostly manuscript form with a little bit of outline in places where I was extemporaneous.
TITLE: The Well-Ordered Life
SCRIPTURE: Luke 12:22-34