No.
The absolute value of a number is the value of the number ignoring the sign - it is always positive:
The absolute value of a negative number is a positive number;
The absolute value of a positive number is a positive number.
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When the absolute value of the positive integer is smaller than the absolute value of the negative one.
When they are added together and the absolute value of the positive integer is bigger than the absolute value of the negative integer or when the negative integer is subtracted from the positive integer.
When the absolute value of the positive integer is the same as the absolute value of the negative one.
The absolute value of an integer is the integer with a positive sign.
The absolute value of a positive integer is positive. When taking the absolute value of any integer, one is essentially removing the sign (whether positive or negative), always leaving the remaining number positive.