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## Homework Statement

1) 100 of the 5-element subsets of {1, . . . , Y } have the same SUM. (Fill in Y . Make Y as small as you can, however you need NOT prove that it is smallest possible. You might

need a calculator.)

2) Let FUNC be the set of all FUNCTIONS from N to N. Show that FUNC is NOT countable.

## Homework Equations

Pigeonhole principle.

## The Attempt at a Solution

1) The only thing I know is that I need to apply pigeonhole principle... Can someone give me a nudge?

2) Definitely confused here. Since the integers are countable, the naturals must be countable too right? THen how the heck are I supposed to show that FUNC isn't countable when it is?