History of Number Systems
An early ancient herdsman once compared his herd's sheep or cattle to a pile of stones when the herd went off to graze and again when it came back to check for any missing livestock. In the earliest system probably the vertical strokes or bars such as "$|,$ $||,$ $|||,$ $||||,$" etc., were used for the numbers "$1,$ $2,$ $3,$ $4,$" etc. Many people, notably the ancient Egyptians, used the sign "$|||||$" to represent the number of fingers on one hand.
Around "$5000 B.C$", the Egyptians had a number system based on "$10$". The symbol "$ก$" for "$10$" and "$੭$" for "$100$" was used by them. The symbol was repeated as many times as it was needed.
For example: the numbers "$13$" and "$324$" were symbolized as "$ก|||$" and "$੭੭੭กก||||$" respectively.
It was determined that the sign "$੭੭੭กก||||$" meant "$100$ $+100$ $+100$ $+10$ $+10$ $+1$ $+1$ $+1$ $+1$." Different people invented their own symbols for numbers. But these systems of notations proved to be inadequate with the advancement of societies and were discarded. Ultimately the set is the counting set (also called the set of natural numbers).
The solution of "$x+2$ $=0$". wasn't possible in the set of natural numbers, therefore the natural number system was extended to the set of whole numbers.
No number within the set of whole number $W$ could satisfy the equation $x+4=2$ or $x+a$ $=b$, if $a>b$ and $a,$ $bϵW$. The negative integers $-1,$ $-2,$ $-3,...$ were introduced to make the set of integers $Z$ $={0, ±1, ±2, ±3,...}$. Again the equation of the type $2x$ $=3$ or $bx$ $=a$ where $a, bϵZ$ and $b≠0$ had no solution within the set of $Z$, so the numbers of the form $\frac{a}{b}$ where $a,$ $bϵZ$ and $b≠0$, were invented to rid of such difficulties.
The set $Q$ $=\{\frac ab|a, bϵZ ˄ b≠0\}$ was named because of the set of rational numbers.
Still, the answer of the equation such as $x^2$ $=2$ or $x^2$ $=a$ (where $a$ is not a perfect square) was not possible in the set $Q$ so the irrational numbers of the type $±\sqrt{2}$ or $±\sqrt{a}$ where $a$ is not a perfect square were introduced.
This process of enlargement of the number system ultimately led to the set of real numbers $(R=Q∪Q'$ is the set of real numbers$)$ which is used frequently in everyday life.
Importance of Numbers
- A number system is a set of numbers used to count, compare and calculate, etc,..
- A set of values used to represent a quantity is defined by a number system.
- Numbers are used for counting and measuring distances.
We speak about
$i)$ The number of students attending class.
$ii)$ The number of pens, has you?
clock times, calendar, year, marks, weight, and height.
Ancient History of Numeration System
- Thousands $(1000)$ of years ago there was neither clock nor a calendar to trace the keeping of time.
- The sun and moon won't identify whether it is morning time or evening time.
- People at that time used tally marks $(||||,$ $||||,$ $||||,$ $||||)$ to representing the passing time.
- These tally marks are also used for counting the number of days and keeping records of quantities.
- They were also known to be using fingers, sticks, or stones to count things.
- But these methods couldn't work for the larger values.
Centuries Later Barter System Started
- When people started exchanging things and which is when they realize the need for numbers.
Invention of Numbers
Babylonian numerals, Chinese numerals, Egyptian numerals, and Roman numerals are different numerals from one another they can not understand numerals each other they have many difficulties understanding their numerals so they need such numerals that they can understand each other numerals easily and they must be common.
- The number system we have today is commonly called Hindu-Arabic numerals.
- The Arabs popularise these algorithms, but their origin goes back to the Phoenician merchants that used them to count and do their commercial countability.
- Have you ever asked the question of why $1$ is "one", $2$ is "two", and $3$ is "three"....?
- What is the Arabic algorithms' underlying logic?
Very Easy
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