Unformatted text preview: 4. Prove that there are an uncountable number of total functions from N to {0, 1} . 5. Give a recursive definition of multiplication of natural numbers using the successor function and addition. 6. Prove that if X and Y are countable sets, then so is X Y. 7. Express using a concise mathematical statement the function from N to N N in Example 1.4.2. 8. Prove Theorem 1.4.2 (SchrderBernstein). 9. Let R be the relation on N + N + given by (a,b) R (c,d) iff a/b = c/d. Show that R is an equivalence relation. What are its equivalence classes? NOTE: Your problem solutions are due at 5:00 pm of the date....
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 Spring '08
 Ehrich,R
 Natural number, Rational number, nonnegative rational numbers

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