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We know that set of natural numbers is the proper subset of integers. Then why the discrepancy occurs in mathematics that there is a bijection between these two sets. I know about such bijective maps but how to convince our mind to accept this fact?

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closed as unclear what you're asking by Lord Shark the Unknown, José Carlos Santos, Andrés E. Caicedo, mechanodroid, Harambe Nov 9 '17 at 22:12

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    $\begingroup$ Um, we prove it. It is important as a first step in understanding infinite cardinals that $A\subsetneq B$ does not mean $A$ has smaller cardinality. $\endgroup$ – Thomas Andrews Nov 9 '17 at 19:21
  • $\begingroup$ Hmm thanks @Thomas $\endgroup$ – Miller Nov 10 '17 at 17:39