For a set to be well-defined, an object must be in the set or not in the set. For example, the set of rugby players at StFX is well-defined. The set of good rugby players at StFX is not well-defined because the notion of "good" is up for debate, it is subjective. We want to avoid situations like that.
There is a famous paradox about a barber that also illustrates what can happen if a set is not well-defined.
Youtube video about Barber paradox
Website explaining the Barber Paradox
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