Important Concepts and Formulas
2. Negative numbers together with whole
numbers are called integers … –3, –2, –1, 0, 1, 2, 3, … are integers.
3. The numbers 1, 2, 3, 4, … are
positive integers and –1, –2, –3, … are negative integers.
4. The number 0 is neither positive nor
negative.
5. The absolute value of an integer is
always positive and is equal to the numerical value of that integer.
6. Every positive integer is greater
than 0 and every negative integer is smaller than 0.
7. The greatest negative integer is −1
and the smallest positive integer is 1.
8. Integers are closed under addition
and subtraction, i.e., if a and b are any two integers, then (a + b) and (a –
b) are also integers.
10. Addition of integers is also associative. For
any three integers a, b and c, we have (a + b) + c = a + (b + c).
11. For every integer, 0 is the identity element under
addition, i.e., a + 0 = a = 0 + a.
12. Integers are closed under multiplication,
i.e., for any two integers a and b, (a × b) is an integer.
13. Multiplication is commutative for integers,
i.e., for any two integers a and b, a × b = b × a.
14. Multiplication of integers is associative,
i.e., for any three integers a, b and c, we have (a × b) × c = a × (b × c).
15. Multiplication of integers is distributive,
i.e., if a, b and c are integers, then a × (b + c) = a × b + a × c and a × (b –
c) = a × b – a × c.