Up | Japanese

Domains of Subjects

Created : 1996-10-17 Updated: 2000-10-17

---

• Here we, for the sake of convenience, divide the contents of the primary mathematics into the following five domains :

Number and Arithmetic Natural Number Rational Number (Fraction, Decimal) Quantity and Measurement Proportional Relation Data Processing Geometry

• As to the first two domains, let us confirm that the number and the quantity cannot be discussed separately. In fact, when we use a system of number, we are treating a system of quantity.
  
  This combination of a system of number and a system of quantity (for example, the weight) occurs in a following way :

This diagram is read :

"B is N times A" "The ratio of B to A is N" "With A being the unit of measurement, the value of B is N"

• The content of the domain of "Proportional Relation" is the "proportional relation/function between two systems of quantity". A general form of this subject is "Relation and Function".
  Other relations/fuctions might be picked up. But they are not important here by themselves.

---

Remark 1
"Measuring a weight B" means


1. Introducing another weight A as the unit
2. Getting the number N which satisfies the following relation :

Indeed, N is called the measured value of B relative to the unit A.


• Remark 2
  The variety of combination between systems of number and systems of quantity may be showed in the form of matrix :

	Number of Apples	Length	Area	Volume	Weight	Time	Temp- rature	Money	2-dim real vector	......
Natural Number	.	.	.	.	.	.	.	.	.	.
Rational Number	.	.	.	.	.	.	.	.	.	.
Real Number	.	.	.	.	.	.	.	.	Multiple	.
Complex Number	.	.	.	.	.	.	.	.	Multiple & Rotation	.
......	.	.	.	.	.	.	.	.	.	.

And, in each combination, the system of number and the system of quantity are factors of a system, which we would like to name "quantity" once again.

The number and the quantity occurs as a set. Therefore, in each domain of "Number and Arithmetic" and "Quantity and Measurement", the instruction becomes a circular argument between these two domains.