en:example
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| en:example [2025/04/08 03:16] – [1.1 TARSKI.miz] superuser | en:example [2025/04/08 03:19] (current) – [1.1.4 Definition of the Union of Sets] superuser | ||
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| \(x, y, z, u, N, M, X, Y, Z\) are arbitrary sets. In set theory, the objects under | \(x, y, z, u, N, M, X, Y, Z\) are arbitrary sets. In set theory, the objects under | ||
| consideration are either sets or their elements; however, sets and elements are not | consideration are either sets or their elements; however, sets and elements are not | ||
| - | formally distinguished. Thus, the term 'set' | + | formally distinguished. Thus, the term “set” denotes an arbitrary object. |
| <mizar ta> | <mizar ta> | ||
| Line 167: | Line 167: | ||
| </ | </ | ||
| - | For any \(X\), the functor (operation) \(\cup X\) is defined as the mapping that associates to \(X\) the set satisfying, for any \(x\) に対して | + | For any \(X\), the functor (operation) \(\cup X\) is defined as the mapping that associates to \(X\) the set satisfying, for any \(x\) |
| \[(x \in \cup X) \Leftrightarrow((\exists Y)(x \in Y \land Y \in X)).\] | \[(x \in \cup X) \Leftrightarrow((\exists Y)(x \in Y \land Y \in X)).\] | ||
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