I'm currently studying for my set theory exam and I got stuck trying to prove that if $2^{\aleph_2} \leqslant \aleph_{\omega}$ then $\aleph_{\omega}^{\aleph_2} = \aleph_{\omega}^{\aleph_0}$. Any help will be much appreciated.
2026-04-02 11:39:13.1775129953
How does $2^{\aleph_2} \leqslant \aleph_{\omega}$ imply $\aleph_{\omega}^{\aleph_2} = \aleph_{\omega}^{\aleph_0}$?
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