I recently bought(adsbygoogle = window.adsbygoogle || []).push({}); Real Analysisby Haaser and Sullivan. Is this a good introductory real analysis book? I really bought it for fun. I'm not going to put a formal real or complex analysis course in my math minor.

Well, I'm on page two at the ordered pair proof.

Why is anorderedpair defined as {{a}, {a, b}} ?

(a, b) = (c, d) if a = c and b = d.

Either {a} = {c} and {a, b} = {c, d}

or

{a} = {c, d} and {c} = {a, b}

I understand the second one. If the two sets are equal, then all of the elements in both sets are the same. So, I guess it's irrespective of the number of elements in each set as long as they're all the same.

For the first one, a = c, and b = c or d. Obviously, if b = d the proof is satisfied. However, why does b equal c or d?

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