Is all of pure mathematics tightly coupled with sets ? I love mathematics but for over 2 weeks now all i have read has been somehow tied with sets. i am having such a hard time dealing with constant involvement of sets and proofs in all the current books. Is there a way to study these subjects without such heavy reliance on sets. I own a few copies of Analysis text books, all use sets left right and center except "A course of Modern Analysis" by E.T. Whittaker and G.N. Watson. Would it be enough for me to just study this book since it goes light on involving sets everywhere instead of Rudin, Royden and binmore's books. ? I am studying towards learning rigorous probability theory, so is there any hope for me to be able to learn measure theory without being driven insane by sets ? I apologize if this question is too vague but i think i am little frustrated with you can guess involvement of sets everywhere.
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What does the "measure" in "Measure theory" measures? It measures sets. You'll be hard pressed to do any measure theory at all without sets.
Actually, as you ask at the beginning of your question, "all of pure mathematics is tightly coupled with sets". Sets became the natural objects to use to define most (if not all) mathematical objects, and that use has only increased along the last 100 years.