hw4-solutions

# Thus we could construct a list of the triplets by

• Notes
• 2

This preview shows page 2. Sign up to view the full content.

Thus we could construct a list of the triplets by first writing down all those that sum to 3, then to 4, then to 5, and so on; such a list would begin (1 , 1 , 1) , (2 , 1 , 1) , (1 , 2 , 1) , (1 , 1 , 2) , (3 , 1 , 1) , (2 , 2 , 1) , (2 , 1 , 2) , (1 , 3 , 1) , (1 , 2 , 2) , (1 , 1 , 3) , (4 , 1 , 1) , (3 , 2 , 1) , . . . These are not the only possible lists. 8. If we had n circles, then we could color them in 2 n ways. For example, if there were four circles to be colored, then we could color them in 16 ways. 2 n is so much larger than n that it starts to seem reasonable that maybe 2 | N | is larger than | N | , where | N | is the cardinality of the natural numbers. In fact it is; the set of all possible circle colorings has the same cardinality as the set of real numbers, which is much larger than the cardinality of the naturals. (Circle colorings, in fact, are secretly just binary expansions of real numbers.) 2
This is the end of the preview. Sign up to access the rest of the document.
• Summer '09
• Lugo
• Math, Real Numbers, Decimal, Natural number, Rational number, Countable set

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern