Mr Cantor has an infinitely large (clean) chalkboard and can write infinitely fast. (a) At 1...

 

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Mr Cantor has an infinitely large (clean) chalkboard and can write infinitely fast. (a) At 1 minute to 12 o'clock he writes the numbers 1 and 2 on the chalkboard and then erases the number 1. At minute to 12 he writes the numbers 3 and 4 on the chalkboard and then erases the number 3. At - minute to 12 he writes the numbers 5 and 6 on the chalkboard and then erases the number 5, and so on. What is written on the chalkboard at 12 o'clock? Give a brief justification of your answer. (b) The next day, Mr Cantor starts again with a clean chalkboard. At 1 minute to 12 he writes the numbers 1 and 2 on the chalkboard and then erases the number 1. At minute to 12 he writes the numbers 3 and 4 on the chalkboard and then erases the number 2; at minute to 12 he writes the numbers 5 and 6 and then erases the number 3, and so on. What is written on the chalkboard at 12 o'clock? Give a brief justification of your answer. [Hint: For both of these, try to come up with a bijection between the set of numbers that are erased from the chalkboard and the times at which they're erased.] Mr Cantor has an infinitely large (clean) chalkboard and can write infinitely fast. (a) At 1 minute to 12 o'clock he writes the numbers 1 and 2 on the chalkboard and then erases the number 1. At minute to 12 he writes the numbers 3 and 4 on the chalkboard and then erases the number 3. At - minute to 12 he writes the numbers 5 and 6 on the chalkboard and then erases the number 5, and so on. What is written on the chalkboard at 12 o'clock? Give a brief justification of your answer. (b) The next day, Mr Cantor starts again with a clean chalkboard. At 1 minute to 12 he writes the numbers 1 and 2 on the chalkboard and then erases the number 1. At minute to 12 he writes the numbers 3 and 4 on the chalkboard and then erases the number 2; at minute to 12 he writes the numbers 5 and 6 and then erases the number 3, and so on. What is written on the chalkboard at 12 o'clock? Give a brief justification of your answer. [Hint: For both of these, try to come up with a bijection between the set of numbers that are erased from the chalkboard and the times at which they're erased.]

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a The numbers written on chlakborad is 2468 Since Mr Cantor started off with 12 and h... View the full answer