Ok, so I'm really stupid. I probably have like a negative IQ. But, I don't get it. If sets don't care about the order of their elements, how can you use a set to define the order of a pair? I am not understanding: {a} = {a} and {a,b} = {b,a} correct? Does {{a,b}}={{b,a}}? And, does {{a},{a,b}}={{a},{b,a}}={{b,a},{a}}={{a,b},{a}}? And, if they are all equal, can you write them all those different ways and they still make an ordered pair?
@yunoewig3095
Жыл бұрын
That's right, those are all equal. But you get an ordered pair because a and b are not symmetrical in that set. b only occurs paired up with a, while a also occurs as a standalone. This set is actually the Alexandrov Topology for the total order consisting of two elements. You could in fact represent any partially ordered set using the same technique.
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Ok, so I'm really stupid. I probably have like a negative IQ. But, I don't get it. If sets don't care about the order of their elements, how can you use a set to define the order of a pair? I am not understanding: {a} = {a} and {a,b} = {b,a} correct? Does {{a,b}}={{b,a}}? And, does {{a},{a,b}}={{a},{b,a}}={{b,a},{a}}={{a,b},{a}}? And, if they are all equal, can you write them all those different ways and they still make an ordered pair?
@yunoewig3095
Жыл бұрын
That's right, those are all equal. But you get an ordered pair because a and b are not symmetrical in that set. b only occurs paired up with a, while a also occurs as a standalone. This set is actually the Alexandrov Topology for the total order consisting of two elements. You could in fact represent any partially ordered set using the same technique.