i do not understand how this notation works.

help me please.

Printable View

- September 12th 2009, 09:14 PMKat-Mintersection of union
i do not understand how this notation works.

help me please. - September 13th 2009, 01:08 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 . - September 13th 2009, 02:10 AMKat-M
So if we define = , what is ?

- September 13th 2009, 02:25 AMTaluivren