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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