I encountered idea of considering Sample space $\Omega$ as collection of function so far as I saw.
Can you show the proof of thesis $x \neq \{x\}$? In a book I saw this thesis is included in context of Russell's paradox.
Best regards,
2026-03-25 15:11:04.1774451464
manners of collection
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In general, if $x$ is any non-set object, the fact that $x \ne \{x\}$ is trivial.
Most certainly, if $x$ is a set with $|x| \ne 1$, you also have $x \ne \{x\}$ since the cardinalities differ.
The final case is $x$ is a set with cardinality $1$, i.e. $x = \{a\}$. Can you prove that $\{a\} \ne \{\{a\}\}$?