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The geometric point of view of sets- a set can be viewed as being contained with a closed curve.

1) How does the geometric view of set show the common property among the elements of a set? We can list the members of the set inside a closed curve call it some upper case letter but still the picture doesn't highlight the common definition or property the members share.

My thoughts: We pick any arbitrary region in space, R. In order for an object to be an element ( reside inside R) it has to obey certain rules, in the same way an individual is subject to certain laws of a legal system which must be respected in order to be part of it.

Can we view a set as some in region in space+ preset conditions?

Expanding further, can subsets be viewed as a region within the region of the original set ( conditions of R) + Additional conditions?