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Math Help - Are you allowed to say aleph-0 - 1 = alepha-0?

  1. #1
    Member Last_Singularity's Avatar
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    Are you allowed to say aleph-0 - 1 = alepha-0?

    And I suppose similarly, can you simply invoke something like:

    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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  2. #2
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    Quote Originally Posted by Last_Singularity View Post
    And I suppose similarly, can you simply invoke something like:

    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 | \mathbb{N}\cup \{ \mathbb{N}\} | = |\mathbb{N} |
    Thus, \aleph_0 + 1 = \aleph_0
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