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ronaldor9
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Can a set A be an element of A, or can A be not an element of A? And what would such mean in plain-speak?
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ronaldor9 said:thanks! By the way, why is it that {x: x=x} and {x: x not an element of x} do not constitute a set? The latter I would think would constitute the null set, but apparently this is wrong.
"Set A: Element of Itself" is a concept in set theory where a set contains itself as an element. This means that the set is both a member and a subset of itself.
The meaning behind "Set A: Element of Itself" is a paradoxical concept that challenges traditional set theory. It raises questions about the nature of sets and their relationships to themselves.
One example is the set of all sets, which contains itself as an element. Another example is the set of all non-self-containing sets, which does not contain itself as an element.
"Set A: Element of Itself" is related to other mathematical concepts such as Russell's paradox, which also deals with self-containing sets. It also has implications for concepts like infinity and self-reference.
The implications of "Set A: Element of Itself" in the scientific community are still being debated. Some argue that it challenges the foundations of mathematics and could potentially lead to new discoveries. Others argue that it is a purely theoretical concept with no practical applications.