Complete testing of sort methods

I just recently completed a small project using a few different sorting methods on sets of random data and while doing some research on the sorting methods, I began wondering how I could fully test each sort method to ensure they worked correctly for all conditions/input. Lets use the bubble sort method for example; obviously I could create a set of data, call the sort method, then check if the result is sorted. I might just be naive, but I cannot think of other conditions or types of input might occur that would cause any of the sort methods to not work.

Appreciate the help guys
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