Integers
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This document discusses integers and their properties. It introduces integers and the integer line. It then outlines several principles of integers, including: integers are closed under addition and multiplication; the commutative, associative, distributive, identity, and inverse principles apply. It also discusses the addition, subtraction, multiplication and division of integers, outlining key formulas for each operation with integers.
Integers
- 2. Introduction to integers system At any vhole number a and b if there is a single element is always added up (a + b) which is the whole numbers. It is said that the system of whole numbers is closed under addition. But not also with subtraction and division
- 3. Integer line
- 4. Integers principle Closed under Principle of addition The closed Principle of the multiplication Commutative Principle of addition Commutative Principle of multiplication Associative Principle of addition Associative Principle of
- 5. The left distributive principle of multiplication over addition The right distributive principle of multiplication over addition For every a, with elements 0 in B so a + 0 = a, 0 is called the additive identity element For every a, with element 1 in B such that ax 1 = a, 1 called elements multiplicative identity Feedback (inverse)
- 6. Addition of integers If a and b are positive integers, then (- a) + (-b) = - (a + b) If a and b are positive integers with a <b, then a + (-b) = - (b - a) a+(-b)=-(b-a) kanselasi Principle of addition If a, b, and c integers and a + c = b + c, then a = b
- 7. Subtraction of integers If a, b and k integers, then a - b = k if and only if a = b + k. subtraction in numbers has not minced closed nature, ie if a and b are the numbers count, (ab) there (whole numbers) only if a> b According to the definition of subtraction a - b = k if and only if a = b + k a + (-b) = (b + k) + (-b) = (k + b) + (-b) = k + (b) + (-b) = k + 0 a + (-b) = k k = a + (-b) This indicates that there is an integer k such that a - b = k
- 8. Multiplication of integers formulas : (-a) x b = (-ab) (-a) x (-b) = ab If a, b, and c integers with b 0, then a: b = c if and only if
- 9. Division of integers Formulas: ((-a) : b) x (b) = (-a) (a : (-b)) x b = (-a) ((-a) : b) x (-b) = a (a : (-b)) x (-b) = a ((-a) : (-b)) x b = a ((-a) : ( -b)) x (-b) = (-a)
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