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Math Help - examples, sequences of ordinals

  1. #1
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    examples, sequences of ordinals

    Give examples of strictly increasing sequences of ordinals such that

    \text{lim}_n(\alpha_n + \beta) \not = \text{lim}_n \alpha_n + \beta,

    \text{lim}_n(\alpha_n + \beta_n) \not = \text{lim}_n \alpha_n + \text{lim}_n \beta_n.

    I cannot think any examples that work for this one. The problem is that I can't recall many examples of strictly increasing sequences of ordinals. I need some help on this problem. Thank you.
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  2. #2
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    multiple post

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