- #1
evinda
Gold Member
MHB
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Hey again! (Blush)
I want to show that the set $\{ a, b \}$ is unique.That's what I have tried:
We suppose that $\{a,b\}, \ \{a,b \}'$ are sets, so that each of them has as elements $a$ and $b$ and only these ,and $\{a,b \} \neq \{a,b \}'$.
From the axiom of extensionality, there is, without loss of generality, a $x$, such that:
$$x \in \{a,b \} \text{ and } x \notin \{a,b \}'$$
But.. how can I continue? (Thinking)![Confused :confused: :confused:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
I want to show that the set $\{ a, b \}$ is unique.That's what I have tried:
We suppose that $\{a,b\}, \ \{a,b \}'$ are sets, so that each of them has as elements $a$ and $b$ and only these ,and $\{a,b \} \neq \{a,b \}'$.
From the axiom of extensionality, there is, without loss of generality, a $x$, such that:
$$x \in \{a,b \} \text{ and } x \notin \{a,b \}'$$
But.. how can I continue? (Thinking)