Question: Please answer exercise 4. Also, please write legibly so I can read your work without confusion. Thanks! Exercise 4. Show that the set Q of

Please answer exercise 4. Also, please write legibly so I can read your work without confusion. Thanks!

Exercise 4. Show that the set Q of all rational numbers is equinumerous to the set I of natural numbers . 15. 8 Example . Consider two circles with the same center . but with different radii . Let CI be the smaller circle and let C 2 be the larger one . Then CI is equinumerous to C2. To see this , for each point & on on CI , let f ( ac) be the point where the half -line from p through a meets C 2. ( I recommend that you draw a picture to make sure that you understand the definition of f . ) Then I is a bijection from CI to C2. This was another of the examples discussed by Galileo in Dialogues Concerning Two New Sciences

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