Say I have a price that undergoes some fluctuations, measure in percentage.
Example: Item A costs \$100, and the price is increased by $4.5\%$ four times, and then decreased by $4.5\%$ four times, in that order.
The way I see it, this just means that the final price $F = \$100 \cdot 1.045^4 \cdot 0.955^4$, but since multiplication is commutative, the order of these fluctuations doesn't matter.
Does that mean that we can just consider the set of eight changes, and disregard the order in which they are applied to the price?