Hello!

Please help me prove the following,

Let . Show that there exist infinite such that is constant on all sets of the form where .

Thank you!

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- November 14th 2012, 01:32 PMAlso sprach ZarathustraExistence of constant [TEX]f[/TEX]
Hello!

Please help me prove the following,

Let . Show that there exist infinite such that is constant on all sets of the form where .

Thank you! - November 14th 2012, 01:45 PMemakarovRe: Existence of constant [TEX]f[/TEX]
What is f here?

- November 14th 2012, 02:10 PMAlso sprach ZarathustraRe: Existence of constant [TEX]f[/TEX]
Oh, sorry!

**Edited!**

- November 14th 2012, 02:14 PMemakarovRe: Existence of constant [TEX]f[/TEX]
Are you proving this for some particular f or for all f?

- November 14th 2012, 02:33 PMAlso sprach ZarathustraRe: Existence of constant [TEX]f[/TEX]
Makarov, I'm trying to prove Ramsey theorem:

Let , set collection in size 2 of naturals. So for all function exist infinite such that is constant on all elements - November 14th 2012, 02:37 PMPlatoRe: Existence of constant [TEX]f[/TEX]
- November 14th 2012, 02:47 PMAlso sprach ZarathustraRe: Existence of constant [TEX]f[/TEX]
- November 14th 2012, 03:52 PMPlatoRe: Existence of constant [TEX]f[/TEX]