multiplication and division.

in the cold november rain..
what could be happen if + meet with -.. such an example 2+ -3.. for sure the answer is -1.
from here we conclude that +- would become -. we understand that there are 4 rule as followed:

1) ++ = +
2) +-  = -
3) -+ = -
4) --  = -

did we ever think about multiplication and division on the same cases as above, what would be happen if the do meet one another. The answer are lie on the number operation itself.  such case for instance is 2x(3/8) = 2x3/8.. the case can be simplified like the subtraction and addition as an properties above.

1) xx = x

2) x/ =  /

3) /x = /

4) // = x

simple thought of compact set

compact set is like a partition2 of main set..

the set can be call compact if the partition of the set a belong to the partition of partition..

a is compact..
bi is partition of a.
ci is a partition of bi..
so from here we can see the hierarcical start from a to b to c. 

determinant. what does the value mean. matrices

the construction of matrices are hold on simultaneous equation that existed in linear stated.
for a simultaneous equation that have many variable, the more matrices row or column that will generated.

determinant is a special properties that only matrices possessed it. without determinant, it will be complicated to determine some matrice to be have inverse or otherwise.

determinant that we understand this day, are must be built form (fair and) square matrice. let we ask ourselves, is it impossible for matrices that did't have same row and column to have it (Determinant). we understand well the concept of polynomial, but we fail to adapt it in matrices. it is not compulsory to put x^3 that is coefficied(times) to scalar (number). then by the re-arrangement we will get the same column of matrices, and just put 0 0 0 0 in the row that are lack of be squared matrices.

determinant, is a degree of the intersection between line, field or perhaps space.
determinant is a sort of skewness degree on the geometry representation.
if the value of determinant become biggest, it is supposed to be that the correpondence matrices are sangat tidak parallel. instead, if the values are small, it seem that the simultaneous equation are getting parallel to each other.

triangle inequalities

must be creative if u want ton prove it.

diagram of irrational number

irrational number is defined as a number that dont have the last digit in their writin'. such as pi, surd 2, sin(x). this type of number are categorized to be irrational. why?
becouse it cant be rationalized. or in the same meaning we purposed it to be express as a fraction of two integer.(natural number).

in the existence of line number, it is clear that by the virtue of cartesian coordinate, that the number are cant be picturized in line. it should be express in the square, cylinder or perhaps sphere.

 ya it is true that the number is a single number, regardless of what number either irr or rational. but how to draw 1.000000000000..... and 1.
first insight it's look like a simple matter, but try to think the 1 is not exactly is 1.0000000000.. each number have their own subset (e.g 1.0000000000089 is a subset of 1.000000000008, and 1.1 is a subset of 1) so the line diagram are cant be draw.