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At times we consider only the magnitude of the number without attaching much importance to its direction. Under these circumstances the sign attached with the number becomes redundant. This concept can also be expressed in terms of the absolute value of a number. The absolute value is nothing but the magnitude of the real number. In this context, the absolute value can never be negative as distance cannot be negative. That is |-3| = |+3| = 3.
The same concept when considered in the light of real numbers will be
|-x| = x, if x < 0
|x| = x, if x > 0.
Apart from these sets we also have even numbers, odd numbers, prime and composite numbers. A number is defined as an even number if it is exactly divisible by 2 otherwise, it is an odd number. A number is said to be a prime number if it has its factors as 1 and itself. That is, if we observe the factors of numbers like 2, 3, 5, 7, 11 etc. we find that they do not have other factors other than 1 and themselves. Numbers like 4, 15 and 96 which have factors other than 1 and itself are called composite numbers.
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lecturer notes
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