Naive Set Theory
Section 1 The Axiom of Extension
Belonging (\(\in\)): If \(x\) belong to \(A\) (\(x\) is an element of \(A\), \(x\) is contained in \(A\)), we shall write \(x \in A\).
Inclusion (\(\subset\))
Equality: \(A = B\)
Inequality: \(A \neq B\)
Axiom of Extension. Two sets are equal if and only if they have the same elements.
If \(A \subseteq B\) and \(B \subseteq A\), then \(A = B\)
Reflexive Property. \(A \subset A\).
Proper Subset. \(A \subset B\) but \(A \neq B \to A\) is a proper subset of \(B\).
Set inclusion is antisymmetric
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\(x^4\) \[ x^5 \] Definition
Do Huu Chu
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