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The absolute value of an integer is greater than the integer.

A. TRUE

B. FALSE

Answer

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We know the set of integers contains all the negative numbers, zero and all the positive numbers and can be written as the set \[Z = \{ .... - 3, - 2, - 1,0,1,2,3....\} \]

So, if we look at a real line, integers are extended on both sides.

Now we know that the absolute value of an integer is defined as the numeric value of the integer without considering the sign along with it. Absolute value of an integer \[x\] is denoted by a modulus sign \[\left| x \right|\].

Value of \[\left| x \right| = x\] if \[x\] is positive.

Value of \[\left| x \right| = - x\] if \[x\] is negative.

Absolute value of an integer is always non-negative as the negative sign along with the integer gets removed when we apply modulus to it.

So, the absolute values of integers are represented on a real line from zero to infinity, which means the whole real line except the negative numbers.

If we take an integer \[ - x\], then absolute value of the integer will be \[\left| { - x} \right| = - ( - x) = x\] which is positive. So, we can say the absolute value of an integer is greater than the integer.

If we take an integer \[x\], then absolute value of the integer will be \[\left| x \right| = x\] which is positive. So, we can say the absolute value of an integer is equal to the integer.

From both the above statements we conclude that the absolute value of an integer is greater than or equal to the value of the integer.

So, the statement given in the question is wrong.

So, option B is correct.