Top-down, Bottom-up differences based on personal experience.
Top-down:
A top-down approach (also known as step-wise design) is essentially the breaking down of a system to gain insight into its compositional sub-systems. Example of my experience about this is when I am answering a problem in algebra or any other subjects, my mind thinks fast with higher knowledge when I solve the problem.
Bottom-up:
A bottom-up approach is the piecing together of systems to give rise to grander systems, thus making the original systems sub-systems of the emergent system. For example when I am buying in the grocery with my mother, she's always taking up too much of her time. Because she's looking up wisely for every detail of the thing she will buy.
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