i do not understand how this notation works.

help me please.

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- Sep 12th 2009, 10:14 PMKat-Mintersection of union
i do not understand how this notation works.

help me please. - Sep 13th 2009, 02:08 AMTaluivren
Hi, i don't know if the following visualisation is helpful:

but maybe this little proposition will make things clear:

Proof: "=>" assume for only finitely many , let be the biggest such , then for all we have . This means , so .

"<=" assume , this means there's some such that , that is, for all , so belongs to only finitely many . - Sep 13th 2009, 03:10 AMKat-M
So if we define = , what is ?

- Sep 13th 2009, 03:25 AMTaluivren