homework05 - Math 5020 Homework 5 due Friday, April 8, 2011...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 5020 Homework 5 due Friday, April 8, 2011 Assume ZFC Regularity. 1. Let X and Y be sets. Show that (a) | X | = | Y | iff | X | e = | Y | e . (b) | X | ≤ | Y | iff | X | e ≤ | Y | e . (c) | X | ≤ | Y | iff there is a function f : Y X with rng( f ) = X . 2. Show that the set of all functions f : R R has cardinality 2 2 0 . ( Hint : You may use the fact | R | = |P ( ω ) | .) 3. Show that the set of all continuous functions f : R R has cardinality 2 0 . ( Hint : A continuous
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online