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This is a follow to a question I had previously asked but got no clarification.

Suppose you wish to find $R^2$ for the relation defined $xRy$ iff $x-y=c$.

I know that $R^2$ is $x-y=2c$, but I'm not sure how that's calculated. If your relation is based on a function then wouldn't this be okay to say: $f(x)= x-y-c$ and so $f(f(x))$ would be a way to calculate it? Although this was my first thought, it turned out that $f(f(x))=x-2y=2c$ which of course is wrong. So how would you define $R^n$ for example?

It is said that it can be calculated using the Boolean product of your matrix, but I don't see how.

Dimitri
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    I discussed it fairly thoroughly in this answer to a question that included this one. This question is really a duplicate of part of that one. – Brian M. Scott Dec 01 '13 at 06:34
  • @BrianM.Scott it seems that everyone in my class is familiar with this site. Thank you. – Dimitri Dec 01 '13 at 06:35
  • @BrianM.Scott one question in regards to your explanation. How do you define the transitive closure on something that's not finite? It seems the higher the $n$ value for $R^n$, the closer your set becomes transitive. Wouldn't $R^*$ simply be $\bigcup_{n=1}^\infty R^n$ ? – Dimitri Dec 01 '13 at 07:33
  • Yes, that’s exactly what $R^$ is. If $R$ is finite, there is always an $m$ such that $R^n=R^m=R^$ for all $n\ge m$, so that you reach $R^*$ after finitely many stages, but if $R$ is infinite, you may need the whole thing. – Brian M. Scott Dec 01 '13 at 07:39
  • Those were my thoughts exactly. – Dimitri Dec 01 '13 at 07:46

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