Question

what is meant by a partition on the interval [a,b]?

Answer 1

partitions divide things up; room partitions divide up a room for instance

Answer 2

the partition of an interval need not be constant; but it helps

Answer 3

partitions of the interval from a to b usually denote a change in "x" notated as: \[\Delta x\]

Answer 4

when \(\Delta x\) is as small as it can be, infinitesimal even, it becomes the calculus equivalent of "dx"