Absolute value can be used as distances, because if an object is either 1 foot behind or 1 foot in front of another object, their distance will still be 1.
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The absolute value of -13 would be 13. This is used in math.
It's not. Unless you add a direction to speed it will not become velocity. Since positive and negative are sometimes used to denote direction, absolute value of velocity may equal speed (certain situations)
Two vertical lines, one on either side of the number.
they aren't used in real life, not unless you need them in a situation were you would need to use them.
natural numbers are used in real life for counting, adding, subtracting and even for calculting money purposes