Thursday, February 23, 2006

Trivial cases

One way of studying a new piece of abstract mathematics, say algebraic topology, is to study the trivial cases or models. One might study the real line or the plane as examples when taking up algebraic topology.

This turns out to be trivial and uninteresting work, but it has one virtue. If you don’t understand why those cases are trivial, then you probably won’t understand the more difficult problems and theorems either.

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