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countable_intersection [2013/09/06 22:04] 127.0.0.1 external edit |
countable_intersection [2014/03/21 11:11] (current) |
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===== Countable intersection ===== | ===== Countable intersection ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $X$ | | + | | @#55CCEE: context | @#55CCEE: $X$ | |
- | | @#88DDEE: $A\in \mathrm{Sequence}(X)\ \lor\ A\in\mathrm{FinSequence}(X)$ | | + | | @#55CCEE: context | @#55CCEE: $A\in \mathrm{Sequence}(X)$ | |
- | | @#88DDEE: $n\in \mathbb N\cup\{\infty\}$ | | + | | @#55CCEE: context | @#55CCEE: $n\in \mathbb N\cup\{\infty\}$ | |
- | | @#FFBB00: $\bigcap_{j=1}^n A_j \equiv \bigcap A(\mathrm{range}(n))$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\bigcap_{j=1}^n A_j \equiv \bigcap A(\mathrm{range}(n))$ | |
==== Ramifications ==== | ==== Ramifications ==== | ||
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=== Refinement of === | === Refinement of === | ||
[[Arbitrary intersection]] | [[Arbitrary intersection]] | ||
- | === Context === | + | === Related === |
- | [[Sequence]], [[Finite sequence]] | + | [[Sequence]] |