I've been working with ordinals recently and was wondering how to think about the size of some ordinals relative to others. For example, $\omega < \omega +1$ as ordinals, but they have the same cardinality, so they are the same "size". So, what is really meant by saying $\omega < \omega +1$? Is it appropriate to think of $\omega +1$ as being "bigger" than $\omega$? I am just trying to get some intuition for situations like this. Any help is appreciated.
closed as unclear what you're asking by Andrés E. Caicedo, Xander Henderson, bof, user91500, Claude Leibovici Sep 24 '17 at 9:16
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