SolitaryRoad.com

Website owner:  James Miller


[ Home ] [ Up ] [ Info ] [ Mail ]

            THE NUMBER SYSTEM IS A CREATION OF MAN





To quote Leopold Kronecker in regard to our number system: "God made the integers. All the rest are the work of man". The number system of classical algebra is a creation of man. It is a man-made edifice devised and defined in such a way that the rules of classical algebra would hold over it. The only numbers that were not created by man are the positive integers 1, 2, 3, .... . All the rest, the positive rationals, the negative numbers, the complex numbers, etc. are all creations of man. The integers have a natural intuitive meaning. Using the integers as building blocks man invented the positive rational numbers as a means for designating measures of continuous quantities. Thus the positive rationals can be given an easy intuitive interpretation as a measure of some continuous quantity (i.e. distance, area, volume, time, etc.). The negative numbers may have intuitive interpretations in some applications (i.e. negative temperatures, debits in accounting, etc.). As far as an intuitive interpretation for the complex numbers is concerned, I am not aware of any. As far as I know they are just very abstract mathematical entities created by man, without any physical or intuitive interpretation. One can ask the question, "What is an integer? (such as the integer "5" or the integer "8") and then answer the question in about the same way as he would the question, "What is a horse?" It has a definite, concrete meaning and he knows what it is. But if he asks, "What is a negative integer? (such as the number "-5" or "-8") the answer is more difficult. A negative integer is more abstract, just a defined mathematical entity, although it may have intuitive interpretations in some instances. If one asks, "What is a complex number?" the answer is that it is just a very abstract mathematical entity with no concrete meaning or interpretation. It is an entity that mathematicans work with without knowing what it is. It is an entity defined by them but lacking an intuitive interpretation. Thus we have intuitive interpretations for some kinds of numbers but not others. In the same way, among the operations on numbers (addition, subtraction, multiplication and division), some operations have physical interpretations and some don't. The sum of two positive numbers has a natural meaning, a natural intuitive interpretation. Subtracting a smaller positive number from a larger one has an intuitive interpretation. The product of a positive number times a positive number has a intuitive interpretation. The division of a positive number by a positive number has an intuitive interpretation. When negative numbers are involved in operations there may be intuitive interpretations and there may not.

 

The concept of the rational numbers starts with the idea of "the n-th part of unity" (i.e. 1/n). Any positive integer "m" times the n-th part of unity gives us the positive rationals (i.e. denoting the n-th part of unity by "n*" any rational number is given by m(n*), where m and n are arbitrary positive integers).


Why are the rules of classical algebra what they are? They are what they are because of the way the number system over which they operate was defined.


Man first created the number system of classical algebra then he went on to devise other number systems for other "number-like" entities such as vectors, matrices, etc. -- setting up rules of operation for them. Thus he broadened and generalized his concept of "number" as well as his concept of "operation".




More from SolitaryRoad.com:

The Way of Truth and Life

God's message to the world

Jesus Christ and His Teachings

Words of Wisdom

Way of enlightenment, wisdom, and understanding

Way of true Christianity

America, a corrupt, depraved, shameless country

On integrity and the lack of it

The test of a person's Christianity is what he is

Who will go to heaven?

The superior person

On faith and works

Ninety five percent of the problems that most people have come from personal foolishness

Liberalism, socialism and the modern welfare state

The desire to harm, a motivation for conduct

The teaching is:

On modern intellectualism

On Homosexuality

On Self-sufficient Country Living, Homesteading

Principles for Living Life

Topically Arranged Proverbs, Precepts, Quotations. Common Sayings. Poor Richard's Almanac.

America has lost her way

The really big sins

Theory on the Formation of Character

Moral Perversion

You are what you eat

People are like radio tuners --- they pick out and listen to one wavelength and ignore the rest

Cause of Character Traits --- According to Aristotle

These things go together

Television

We are what we eat --- living under the discipline of a diet

Avoiding problems and trouble in life

Role of habit in formation of character

The True Christian

What is true Christianity?

Personal attributes of the true Christian

What determines a person's character?

Love of God and love of virtue are closely united

Walking a solitary road

Intellectual disparities among people and the power in good habits

Tools of Satan. Tactics and Tricks used by the Devil.

On responding to wrongs

Real Christian Faith

The Natural Way -- The Unnatural Way

Wisdom, Reason and Virtue are closely related

Knowledge is one thing, wisdom is another

My views on Christianity in America

The most important thing in life is understanding

Sizing up people

We are all examples --- for good or for bad

Television --- spiritual poison

The Prime Mover that decides "What We Are"

Where do our outlooks, attitudes and values come from?

Sin is serious business. The punishment for it is real. Hell is real.

Self-imposed discipline and regimentation

Achieving happiness in life --- a matter of the right strategies

Self-discipline

Self-control, self-restraint, self-discipline basic to so much in life

We are our habits

What creates moral character?


[ Home ] [ Up ] [ Info ] [ Mail ]