Hi.

Could you give me a hint how to solve this problem?

Let .

Check if is injective or surjective.

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- January 11th 2013, 02:58 AMwilhelmFunction assigning each subset of R sum of its elements
Hi.

Could you give me a hint how to solve this problem?

Let .

Check if is injective or surjective. - January 11th 2013, 03:17 AMemakarovRe: Function assigning each subset of R sum of its elements
There are two mistakes here. First, D is the collection of

*finite*nonempty subsets of , so . Second, pigeonhole principle is not valid for infinite sets. You may have an injection from a infinite set into its proper subset; in fact, this is one of the definitions of an infinite set. The proof of the pigeonhole principle proceeds by induction on the cardinality of the domain, so it only applies when this cardinality is a natural number. You need to use transfinite induction to prove properties of infinite numbers (ordinals). It is probably instructive to see where the proof of the principle breaks down when one tries to use transfinite induction instead of regular one.

Speaking about the problem, you need to have an intuition about D. Can you give examples of sets in D? Both questions are trivial once you understand what D is. - January 11th 2013, 04:05 AMwilhelmRe: Function assigning each subset of R sum of its elements
Thank you, I've already deleted that comment. Could we just say that for example and for example ?

Or is it oversimplified? - January 11th 2013, 04:15 AMemakarovRe: Function assigning each subset of R sum of its elements
- January 11th 2013, 04:35 AMwilhelmRe: Function assigning each subset of R sum of its elements
Thank you. Could you maybe help me with the linear algebra problem about detA=1995, too?

http://mathhelpforum.com/advanced-al...tml#post763331