We can see the mathematics as a science. As a science, Mathematics has objects. The object of mathematics is the material object and formal object. Mathematics material objects are in our minds. We can only imagine the object of mathematics in our minds, because the object of mathematics is abstract, different with the other sciences which is usually the material object is the concrete object as in our daily life.
Mathematics has been called "the queen of the sciences" and also their handmaiden and since its essential character is so very poorly understood by many, it seems desirable to delve into the mysteries of this subject. In the first place mathematics is much more than the art of computation.
"Studying mathematics" was the reply. "Studying nothing but mathematics for three years" exclaimed his friend as he gazed at a brick wall across the street, "why I suppose you could count the bricks in that wall at a glance."
This illustrates a popular misconception in regard to the nature of mathematics. To be able to compute with ease and to perform a few simple mathematical tricks is often taken to mean that one is gifted in mathematics. In fact, some noted mathematicians have been rather slow at numerical computation.
Every subject in school curriculum has its own objectives and structure. Mathematics helps in making base and structure of many subjects. Mathematics is an important component of school education and that is why it has become a compulsory subject in school curriculum.
A fair competence in manipulation is admitted to be a necessary prerequisite to understanding a mathematical argument. But no amount of technical facility will of itself teach anyone what mathematics is or what proof means; nor will it suggest what is probably the most important reason why mathematics is today an even more vital human need and social necessity than it was in the past. Manipulative skill may suffice for the average technician in the trades but it is inadequate as an aid to self-respecting citizenship in even a moderately intelligent society.
The Babylonian system of writing was called cuneiform and was based on a series of straight lined symbols. These symbols were wet and baked in the hot sun to preserve. Curved lines could not be drawn. These cuneiform symbols led to many tables used to aid calculation. As stated previously, they used a base 60 system, which has ten proper divisors, instead of our current system, base 10 with only two proper divisors.
Egyptians and Romans: Number System
The Roman and Egyptian systems did not make Arithmetic calculations easy. Multiplication of Roman numerals is nearly impossible and exceedingly complex. Unlike the Babylonians, the Egyptians did not develop fully their understanding of mathematics. Instead, they concerned themselves with practical applications of mathematics.
Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available are Plimpton 322 (Babylonian mathematics ca. 1900 BC), the Moscow Mathematical Papyrus (Egyptian mathematics ca. 1850 BC), the Rhind Mathematical Papyrus (Egyptian mathematics ca. 1650 BC), and the Shulba Sutras (Indian mathematics ca. 800 BC). All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
Natural Numbers
"Natural Numbers" can mean either "Counting Numbers" {1, 2, 3, ...}, or "Whole Numbers" {0, 1, 2, 3, ...}, depending on the subject.
Integers
Integers are like whole numbers, but they also include negative numbers ... but still no fractions allowed!.
A rational number is a number that can be written as a simple fraction (i.e. as a ratio). a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with thedenominator b not equal to zero. Since b may be equal to 1, every integer is a rational number. A rational number is a number that can be expressed as a fraction
where 
and 
are integers and 
. A rational number is said to have numerator and denominator . Numbers that are not rational are called irrational numbers. SEE IN STET BOOK PUBLISHED BY PASRICHA PUBLICATION, JALANDHAR
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