Why in module inequality | f ( x ) | < A with a positive A we do not explicitly

Makayla Boyd

Makayla Boyd

Answered question

2022-06-28

Why in module inequality | f ( x ) | < A with a positive A we do not explicitly check that f ( x ) >= 0 and f ( x ) < 0?
| f ( x ) | < A when А > 0 is equivalent to the following system:
{ f ( x ) < A f ( x ) > A
I do not completely understand, why we do not exclude those x, for which f ( x ) < 0 in the first equation, and x for which f ( x ) < 0 in the second equation - I mean why we do not write explicitly two systems of inequalities, uniting their solutions like this:
{ f ( x ) < A f ( x ) >= 0
{ f ( x ) > A f ( x ) < 0

Answer & Explanation

Carmelo Payne

Carmelo Payne

Beginner2022-06-29Added 25 answers

The two systems are completely equivalent.
In the first you find directly all solutions by intersection of two inequalities, in the second case by union of two different systems of inequalities.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?