Math 332 Test 1 Name




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Math 332

Test 1

Name________________________


1. Give the definition for a set S to be infinitely countable.
2. Is the set S = { 3, 7, 11, 15, ….} countable? If so prove it; if not, prove it.


3. Is the set of real numbers in the interval [0,1] countable? If so, prove it, if not, prove it.


4. Does 6 | 7n-1 for n > 1 , where n is a natural number ? If so, prove it; if not, prove it.

5. Does 3| 4n –1 for n >1, where n is any natural number? If so, prove it. If not, prove it.

6. Find a base 10 representation for the base 3 number .221122112211…

7. Is any repeating sequence of decimal digits a rational number? If so, prove it; if not, prove it.


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