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grothendieck_universe [2014/12/10 11:14] nikolaj |
grothendieck_universe [2015/08/24 19:32] nikolaj |
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| @#55EE55: postulate | @#55EE55: $Y \subseteq {\mathfrak G} \implies Y\ {\approx}\ {\mathfrak G}\lor Y \in {\mathfrak G} $ | | | @#55EE55: postulate | @#55EE55: $Y \subseteq {\mathfrak G} \implies Y\ {\approx}\ {\mathfrak G}\lor Y \in {\mathfrak G} $ | | ||
- | ==== Discussion ==== | + | ----- |
- | === Formalities === | + | === Discussion === |
+ | == Formalities == | ||
The symbol ${\approx}$ in the last postulate is an abbreviation. For subsets $Y$ of ${\mathfrak G}$, equinumerosity can be defined as the existence of a set of pairs, $f=\{\{y,u\},\{y',u'\},\dots\}$, which puts elements $y\in Y$ uniquely in correspondence with $u\in{\mathfrak G}$: | The symbol ${\approx}$ in the last postulate is an abbreviation. For subsets $Y$ of ${\mathfrak G}$, equinumerosity can be defined as the existence of a set of pairs, $f=\{\{y,u\},\{y',u'\},\dots\}$, which puts elements $y\in Y$ uniquely in correspondence with $u\in{\mathfrak G}$: | ||
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nLab: | nLab: | ||
[[http://ncatlab.org/nlab/show/Grothendieck+universe|Grothendieck universe]] | [[http://ncatlab.org/nlab/show/Grothendieck+universe|Grothendieck universe]] | ||
- | ==== Parents ==== | + | |
+ | ----- | ||
=== Requirements === | === Requirements === | ||
[[Bijective function]], [[Power set]] | [[Bijective function]], [[Power set]] |