Also, it says, when proving vacuously (not sure how that's pronounced), that we pick an arbitrary element from P(x) and prove that it satisfies Q(x). But doesn't that just prove that the statement is true for that element? How does that prove the rest will satisfy the statement as well?
Interesting: I am excited to start doing proofs! I find it interesting how they never take anything for granted. I mean, they even started with proving if a number was even or odd, using only three base rules. It's so fascinating how pretty much everything we know in math, no matter how simple or complex, is derived from a proof. If you think about a Calculus proof, it probably is based upon several algebra proofs, which are based upon other proofs, which could be based on others. It's like a family tree of proving stuff in here!!
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