Let A={a_1,a_2,a_3,...} be a countably infinite set, and let A'=A-{a_1}. Prove that |A|=|A'|.
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Originally Posted by natewalker205 Let A={a_1,a_2,a_3,...} be a countably infinite set, and let A'=A-{a_1}. Prove that |A|=|A'|. Hint: $\displaystyle f:A \to A',f(a_i) = a_{i+1}$ is a bijection.
i can't get the onto part of the bijection
Originally Posted by natewalker205 i can't get the onto part of the bijection Let $\displaystyle a_k \in A'$, $\displaystyle a_{k-1} \in A$. This is meaningful because k > 1.
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