Canter's method

  1. Can anybody tell me the Canter Method of proving that certain sets are infinite? It is called as "Diagonal Method".
     
  2. jcsd
  3. Zurtex

    Zurtex 1,123
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  4. Hey thanks, Zurtex! But from the first link, it does not become clear why it is called "Diagonal Method". Also, can you explain the link between first proof and second proof, please? Also, please tell me how to construct a bijection between Rationals & Reals.
     
  5. shmoe

    shmoe 1,994
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    See the wiipedia article, step 5 in the proof singles out the 'diagonal' terms of the list. I only count one proof in the links he gave.

    There isn't one. The diagonal argument shows the reals are uncountable while the rationals are countable.
     
  6. Oh! I'm sorry for saying reals & rationals! It's integers and rationals! And why do you count only one proof?
     
  7. matt grime

    matt grime 9,395
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    The rationals are famously countable, try constructing the proof yourself. There are two variants. One is anothert kind of diagonal argument, and the other is by remembering that rational numbers are a subset of the pairs of integers.
     
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