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I have two partition, P= {$x_0,x_1,...,x_n$} and Q= {$y_0, y_1,...,y_n$}. P is a general partition of the interval of [a,b] and Q is a fixed partition of [a,b].

What does it mean for Q to be fixed? Does the number of points, n, in Q have to remain the same but the number of points, n, in P can vary even though they use the same subscript? Does P and Q have to have the same number of points, n, but the distances in Q are fixed?

I've tried googling an answer but I keep getting computer memory partition results and my notes/textbook don't have a definition either.

Does someone have a definition they can give me?

Thank you

Tim
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1 Answers1

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I'd need a bit more context, but my guess would be that $P$ is actually not one thing, but rather a family of partitions which changes when you change some parameter(s) in the problem. (For example, in integration we always eventually send the number of subintervals $n$ to $\infty$, so it makes sense to parametrize partitions by this number.) In this case it would be more correct to write $P(n)$ or $P_n$, but for ease of notation we often suppress this sort of dependence.

Saying that $Q$ is fixed is specifically saying that it isn't like this, i.e. it doesn't depend on anything.

Ian
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