18. maj 2009 05:54
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Way back when I was a math-major at university, we were taught about "operations on sets". A *set* could simply be "the natural numbers", which could be defined as all positive integers including the number 0. An *operation* on this set could be addition of numbers, multiplication of numbers and so forth. An operation can have a lot of characteristics, e.g "commutative", "associative" or "transitive". An "associative" *operator* means that you can *group the **operands* any way you want* *and a "commutative" operator means that you can change the order of the *operands*. Confused? Well, it's not that complex when you think of it. The mathematical operator "addition" is an "associative" operator (or "relation") since (1+2) + 3 = 6 and 1 + (2+3) = 6. The operator "divide" is __not__ associative since (1/2) / 3 = 1/6 whereas 1 / (2/3) = 3/2. Addition is also a commutative property since you can change the order of the numbers being added together. This is evident since 1+2+3 = 6 and 3+2+1 = 6. Similarly "subtraction" is not a commutative operator since 1-2-3 = -4 whereas 3-2-1 = 0.

The transitive characteristic is a bit different than this and the "everyday equivilant" would be when we *infer* something. So think of transitivity is a mathematical formulation of what we do when we *infer*.

The relation "is greater than" is a transitive characteristic - as well as "is equal to". Basically, a relation (is greater than) being transitive means, that if A > B and B > C then A > C.

The latter popped into my mind the other day when I was pondering over interoperability between implementations of document formats.

Ever since Rob's ingenious article "Update on ~~OpenOffice.org Calc~~ ODF interoperability", I haven't been able to get it out of my head.

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