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| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
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empty_set [2015/10/08 20:32] nikolaj |
empty_set [2015/10/08 20:33] nikolaj |
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| Line 15: | Line 15: | ||
| $\exists! y.\,y=\{x\mid \bot\}$ | $\exists! y.\,y=\{x\mid \bot\}$ | ||
| - | holds, really is an abbreviation for | + | holds, which really is an abbreviation for |
| $\exists! y.\,\forall x.\,\left(x\in y\Leftrightarrow \bot\right)$ | $\exists! y.\,\forall x.\,\left(x\in y\Leftrightarrow \bot\right)$ | ||
| Line 49: | Line 49: | ||
| Uniqueness is discussed, for example, in | Uniqueness is discussed, for example, in | ||
| - | [[https://proofwiki.org/wiki/Empty_Set_is_Unique|Empty_Set_is_Unique (Proof Wiki)]]. | + | [[https://proofwiki.org/wiki/Empty_Set_is_Unique|Empty Set is Unique (Proof Wiki)]]. |
| It requires judgements of equality of sets, which is proven via the axiom of extensionality. | It requires judgements of equality of sets, which is proven via the axiom of extensionality. | ||
| Line 61: | Line 61: | ||
| Proof Wiki: | Proof Wiki: | ||
| - | [[https://proofwiki.org/wiki/Empty_Set_is_Unique|Empty_Set_is_Unique (Proof Wiki)]] | + | [[https://proofwiki.org/wiki/Empty_Set_is_Unique|Empty Set is Unique (Proof Wiki)]] |
| ----- | ----- | ||
| === Subset of === | === Subset of === | ||
| [[First infinite von Neumann ordinal]] | [[First infinite von Neumann ordinal]] | ||
