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A person can remember himself at different points in the past. Each of 'himself' that he remembers at each point in the past can also remember a person in the past, and so on.

So if we have a, b, c, d

So

  • c has a direct relation to d
  • b has a direct relation to c and to d
  • b has another relation to d via c
  • a has a direct relation to b, to c, and to d
  • a has another relation to c via b, and to d via b, and to d via b via c

EDIT: Another example would be a military chain of command - The General can command the Colonel directly, and he can command the Private directly, and he can command the Private by way of commanding his Colonel.

What relations would describe the relation in the example?

Hal
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2 Answers2

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The question is asking you to test this relation against the types you know. One is probably reflexive. This requires that for all elements $x$ of the set, we have $xRx$. As we do not have $aRa$, it is not reflexive. Some other types might be symmetric, antisymmetric, transitive, partial order, total order. Look up the definitions and see.

Ross Millikan
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  • It was my own question. I looked up the different kinds of relations, and couldn't find something that fit well. But it seemed to me that the relation would come up often enough that there might be a term to reference it specifically. – Hal Dec 25 '13 at 14:15
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    @Hal: A total order is the most restrictive of the above choices and it satisfies that. It also satisfies some of the others and it would be good for you to figure out which ones. Mathematically, it is also a well order, but I doubt the military can well order anything. – Ross Millikan Dec 25 '13 at 15:28
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Let's call the relation $R$, and the relations we have are $cRd, bRc, bRd, aRb, aRc, aRd$. So, by inspection the relation is transitive.

Christopher Liu
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  • I agree, but I'm hoping there's a way to capture something more specific about this relation. Consider a military chain of command - The General can command the Colonel directly, and he can command the Private directly, and he can command the Private by way of commanding his Colonel. – Hal Dec 25 '13 at 14:22