Thousands of jokes have been told about marriage and divorce. Exercises 61-68 are based on the following observations: • "By all means, marry; if you get a good wife, you'll be happy. If you get a bad one, you’ll become a philosopher. "—Socrates • "My wife and I were happy for 20 years. Then we met."— Rodney Dangerfield • "Whatever you may look like, marry a man your own age. As your beauty fades, so will his eyesight."—Phyllis Diller • "Why do Jewish divorces cost so much? Because they're worth it." — Henny Youngman • " I think men who have a pierced ear are better prepared for marriage. They've experienced pain and bought jewelry." — Rita Rudner • “For a while we pondered whether to take a vacation or get a divorce. We decided that a trip to Bermuda is over in two weeks, but a divorce is something you always have."— Woody Allen In how many ways can these six jokes be ranked from best to worst?
Thousands of jokes have been told about marriage and divorce. Exercises 61-68 are based on the following observations: • "By all means, marry; if you get a good wife, you'll be happy. If you get a bad one, you’ll become a philosopher. "—Socrates • "My wife and I were happy for 20 years. Then we met."— Rodney Dangerfield • "Whatever you may look like, marry a man your own age. As your beauty fades, so will his eyesight."—Phyllis Diller • "Why do Jewish divorces cost so much? Because they're worth it." — Henny Youngman • " I think men who have a pierced ear are better prepared for marriage. They've experienced pain and bought jewelry." — Rita Rudner • “For a while we pondered whether to take a vacation or get a divorce. We decided that a trip to Bermuda is over in two weeks, but a divorce is something you always have."— Woody Allen In how many ways can these six jokes be ranked from best to worst?
Solution Summary: The author explains how the number of ways to rank six jokes can be calculated by multiplying the possibility of numbers at each place.
Thousands of jokes have been told about marriage and divorce. Exercises 61-68 are based on the following observations:
• "By all means, marry; if you get a good wife, you'll be happy. If you get a bad one, you’ll become a philosopher. "—Socrates
• "My wife and I were happy for 20 years. Then we met."— Rodney Dangerfield
• "Whatever you may look like, marry a man your own age. As your beauty fades, so will his eyesight."—Phyllis Diller
• "Why do Jewish divorces cost so much? Because they're worth it." — Henny Youngman
• "I think men who have a pierced ear are better prepared for marriage. They've experienced pain and bought jewelry."
— Rita Rudner
• “For a while we pondered whether to take a vacation or get a divorce. We decided that a trip to Bermuda is over in two weeks, but a divorce is something you always have."— Woody Allen
In how many ways can these six jokes be ranked from best to worst?
Prove that a closed interval [0,1] = {x in R: 0 <= x <= 1} is a closed set by showing that it contains all its limit points
Please answer part a
What is correct: (i) "continuity impies differentiability"; (ii) "differentiability
implies continuity"? For each statement, either provide a brief proof or give a coun-
terexample.
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