The not() function inverts the meaning (and as such; the result) of the argument.
//Sales.Customer[not(Name = 'Jansen')]
This query returns all customers whose names is not equal to ‘Jansen’.
This query returns the same result as:
//Sales.Customer[Name != 'Jansen']
This query returns all customers who have not placed at least one order.
//Sales.Customer[not(Sales.Customer_Order/Sales.Order/TotalPrice > 30000)]
This query returns all the customers who have placed no orders with a TotalPrice of more than 30,000, including those that have not place any orders at all.
This query does not return the same result as:
//Sales.Customer[Sales.Customer_Order/Sales.Order/TotalPrice <= 30000]
This query returns all the customers who have placed at least one order with a TotalPrice of less than 30,000, regardless of the number of orders they have placed worth more than 30,000. For example, if a customer has placed two orders, one for 15,000 and one for 35,000, this query will return this customer, while the not query will not. Customers who have not placed any orders will not be returned by this query.