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At least I need a reference to some book.

Chiranjeev_Kumar
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John
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  • I'm contemplating between closing this as a duplicate, or as lack of context. – Asaf Karagila Aug 29 '15 at 11:26
  • For future reference, always make the body of the post self-contained. As it stands, your post should have been closed for a variety of different reasons (lack of context, unclear, duplicate). But seeing how someone jumped the gun and posted an answer, I figured a duplicate is the most appropriate. In the future, search first, search again, then when your third search came up empty, write a proper question. – Asaf Karagila Aug 29 '15 at 11:29
  • It is my first post ever. I am unexperienced. Please show mercy :) – John Aug 29 '15 at 11:31
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    I would, in general, you should usually look around before you jump into the pool. There might be some rules against jumping in naked. – Asaf Karagila Aug 29 '15 at 11:32

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Consider the mapping $$f: P(\mathbb{N}) \to \{0,1\}^{\mathbb{N}}$$ where $f(A) = (a_n)_{n \in \mathbb{N}}$ is the sequence of zeros and ones such that $a_n = 0$ if $n \notin A$ and $a_n = 1$ if $n \in A$. Now you can show that this is a bijection.

j4GGy
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  • Thank for your response. Please show me why it is a bijection (I am very amateur in set theory).Thank you in advance ! – John Aug 29 '15 at 11:29
  • Right here is where you follow Asaf's advice and read all the related answers that work through this question in detail, rather than asking someone to re-type them so that you don't have to click for 20 seconds. :) – John Hughes Aug 29 '15 at 11:42
  • Ok ! Got it! Thank you guys !!! – John Aug 29 '15 at 11:42