Union and SameTest

Q: I want to apply to a list of real numbers in which many duplicates occur. However, small differences between the numbers cause some of the duplicates to be retained instead of discarded. Suppose the list is

My present method is to apply to the numbers.

Is there a better method?

Adam Strzebonski (adams@wolfram.com) answers: uses to decide which elements should be considered equal. Here is a that does what you want: