SQL: how to omitt “=”, using only BETWEEN operator

We have e.g. next table 'Persons':

Name    Salary    
Jack    500
Joe     1000
Nancy   550
Fiby    700
Max     1100

I want to select persons with salary between borders (500, 1000), using only BETWEEN operator, and selected salaries should be > 500, and < 1000. BETWEEN is shortage of >=, <=, so how to omitt that "="?

(yep, it can be solved e.g. with

SELECT * FROM Persons
WHERE Salary BETWEEN 500 and 1000
AND Salary NOT IN (500, 1000);

But just wondering - is it possible to do such selection with using Only BETWEEN (and 500, 1000 numbers).