Existence proofs seem rather straight forward. I found it difficult to intuitively see the methods for beginning existence proofs, especially those relating to rational and irrational numbers. It took me a little while to understand the example that there exist 2 rational numbers a and b, such that a^b is rational. I will need to get more comfortable with these proofs, as usual, by experience.
I enjoy the thought of disproving existence statements. It requires finding contradictions in the existential case or proving more generalized "for all" statements. I can see that would begin to be quite a powerful tool.
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