Dottie Parra

2020-10-26

Give an example of a refinement in mathematical modeling with contextual explanation.

Malena

Consider the set [0, 1], and consider it's partition $A=\left(0,\frac{1}{4},\frac{1}{2},\frac{3}{4},1\right)$ and consider a refinement of this partition, B Note that refinement of a partition A contains all points of A and possibly some other points, thus B can be considered as: $B=\left(0,\frac{1}{8},\frac{1}{4},\frac{1}{2},\frac{3}{4},\frac{7}{8},1\right)$ Here it can be seen that A is contained in B, i.e. A sub B And if we consider another refinement of A: i.e. ${B}_{1}$
is an refinement of is not an refinement of B.

Do you have a similar question?