Notes while starting to read the textbook for Real Analysis at UNC (which is actually called Advanced Calculus I for some reason).

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What’s the mapping look like for additive identity, additive inverse, multiplicative identity, and multiplicative inverse?

What does a plot of all the irrational numbers look like on a number line? Is it possible to quantify how many irrational numbers there are? (We should know that this is infinite because we know that there are infinitely many primes and therefore infinitely many primes to take the square root of).

Is there a shortcut to proof by cases?

Why does proof by contradiction work?