article - absolute value

Question

Is the article before the absolute value? I know that there is always an article in phrases like the absolute value of sth but I saw the sentence below without any article. Is it right? Thank you

A increases in (the) absolute value as d increases.

Answer 1

Yes.

"Absolute value" here is a property of A. Just as you might say "A increases in redness as d increases", meaning A becomes redder, you can apply that sentence structure to any property.

Using the for "absolute value" is right when you are talking about a particular instance of that property:

The absolute value of A is 7.
The redness of this apple is greater than that one. (Not particularly idiomatic, but valid.)