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I've just begun learning about sets. My first language isn't English.

My textbook defines a set as:

A set is a well-defined collection of objects.

While, others define a set as:

A set is a collection of distinct objects.

To me, both definitions do not look the same. Maybe they mean the same thing, but I am not convinced.

What needs to be well-defined or distinct, the collection or the objects?

What does it mean to be "well-defined" here?

If we are given A={2, f, π, €}, can we say that A is a set? In that case, we know that all the elements of this collection are distinct from each other. But, is this collection well-defined? If it is, then what's its definition?

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