And I suppose similarly, can you simply invoke something like: $\displaystyle 2^N - 1 = 2^N$? I need this fact to be true in order for me to solve a problem. Is it true; may I use this in a proof? Thanks!
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Originally Posted by Last_Singularity And I suppose similarly, can you simply invoke something like: $\displaystyle 2^N - 1 = 2^N$? I need this fact to be true in order for me to solve a problem. Is it true; may I use this in a proof? Thanks! It is true that $\displaystyle | \mathbb{N}\cup \{ \mathbb{N}\} | = |\mathbb{N} |$ Thus, $\displaystyle \aleph_0 + 1 = \aleph_0$
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