Definition of an ordered pair in Analysis text

Question

In my analysis text the author defines an ordered pair

$$ (a,b) := \{ \{a\}, \{a,b\} \} $$

I am confused as to how this is an adequate definition. I see that it establishes order but other than that I am lost. Any help would be much appreciated.

This is called the Kuratowski definition if you wish to Google it — GFauxPas, Jan 21 '15 at 01:43

score 1 · Accepted Answer · answered Jan 21 '15 at 01:49

The definition guarantees that if two ordered pairs which are not "equal" in an intuitive sense, they are not be equal in the formal sense given by the definition.

So take the pair (1,2) and translate it into a set of sets using the definition. Do the same for the pair (2,1). What difference do you see? Do the same thing with a ordered pair (a,b).

The advantage of such a definition is that you define an ordered pair using an already known concept: sets. You will probably not use this definition often. But if a problem comes up with ordered pairs, you may have to come back to the definition to solve the problem.

Thank you very much for the help! – albertjorlando Jan 21 '15 at 02:58 — albertjorlando, Jan 21 '15 at 02:58

Definition of an ordered pair in Analysis text

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