absolute value
The absolute value is a mathematical function that measures the distance of a number from zero on the number line
The absolute value is a mathematical function that measures the distance of a number from zero on the number line. It is denoted by two vertical bars, such as |x|, where x is the number you want to find the absolute value of.
The absolute value function always returns a non-negative value. If the number inside the absolute value, x, is positive or zero, then the absolute value is equal to x. However, if x is negative, the absolute value will be its positive equivalent. This is because the distance from a negative number to zero is always positive.
Mathematically, the absolute value function is defined as follows:
| x | = x, if x ≥ 0
| x | = -x, if x < 0
To understand this with an example, let's consider two cases:
1. |3|
In this case, the number inside the absolute value function is 3, which is a positive number. Therefore, the absolute value of 3 is equal to 3 itself, because it is already a non-negative value.
2. |-5|
Here, the number inside the absolute value function is -5, which is a negative number. According to the definition, the absolute value of -5 will be its positive equivalent, that is, 5. This is because the distance from -5 to 0 on the number line is 5 units.
In summary, the absolute value function returns the non-negative value of a given number, and if the number is negative, it returns its positive equivalent.
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