What exactly the word 'objects' does mean in the definition of a set, is it an indefinable concept? then how can we say it is a 'well defined object' ? Can I say 'objects' are 'being that exists' in the sence of existence? or Any difficulties to say it can be either a physical entity or an abstract concept?

Also, I have seen that objects are members of set and set is a collection of objects, Is it a circular reasoning?

## Best Answer

We can do math without worrying about what the elements of a set "really are" in a metaphysical sense. What matters is that sets obey certain logical rules (i.e. the axioms of set theory, which are formalized as sentences of first order logic with the symbol $\in$). There's no circularity in stating those axioms and studying their consequences.