ARITHMETIC ASSIGNMENT HELP
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Understanding Arithmetic :- Arithmetic is the branch of Mathematics that handles numbers (from the Greek arithmos = number), you could call it Number Mathematics. It is a branch of mathematics that deals with numbers and operations ( addition, subtraction, division, and multiplication). Brahmagupta, an Indian mathematician and astronomer is the father of Arithmetic. He used zero as separate number and define the results for addition, subtraction, division and multiplication of all other numbers, including zero ( except division by zero).
What Are The Main Elements Of Arithmetic?
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Elementary Arithmetic :- Addition, subtraction, multiplication and division are the four basic operations of elementary arithmetic. They are binary operators. They each take two numbers to produce a third number and are normally written with infix notation :- (Addition a+b) (Subtraction a−b) (Multiplication a×b or a⋅b or ab) (Division a÷b or a/b or ab) The “minus” symbol for subtraction is sometimes used as a unary operator to get the additive inverse of a number. The additive inverse of a number, a, is the number b such that :- a + b = b + a = 0 ⇒ b = −a. We do not have such a handy notation for the multiplicative inverse which is the number b such that :- a × b = b × a = 1 ⇒ b = 1/a so instead we write b=a−1 somewhat abusing the notation for exponentiation which is not considered one of the basic arithmetic operations :- Exponentiation ab= a × a × ⋯ × a .One final aside in regard to division, it is best to consider it to be defined in terms of multiplication and the multiplicative inverse :- a ÷ b ≡ a × b − 1 .There is no multiplicative inverse for the additive identity (zero) so, by definition, division by zero is undefined and meaningless (especially for 0÷0).
Decimal System :- The origin of the decimal system is known to have Indian origin as according to ancient texts written around 300 B.C. a treatise written by the name of Sulba Sutra(book of cords) there are formulas regarding values of π and √2 and areas of circles and figures. That book even contains the formula which is modern-day Pythagoras Theorem (before Pythagoras himself, Indians had the formula).
Number System :- Number System is a set of protocols for using Numbers. Say we have numbers we use from 0 – 9. Now we use these to form different numbers like 22, 33, 45, etc, each number is a combination of two number characters. This is one rule to get a bigger number than 9. Also, we have rules as to what we can do with numbers, say operations. We know there are certain operations like add, subtract, multiply, divide, etc to do manipulations on the numbers, we set those operators to show how we can relate to a real use-case. All these rules and the number set (0–9) form the Number System. This is just a basic introduction, but the depth of the Number System Rules gets Deeper with User Abstraction(An Abstraction is a simplification of a certain Use case).