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The word minimal is confused in more than one way. Please note that there are multiple groups on this page.

minimal the least possible
marginal at the edge of; the least acceptable
small little in value, quantity, or size

Examples  

I made marginal notes on the spreadsheet.
Profits from the enterprise were marginal.
Employees who put in minimal time and effort were laid off.
Profits were too small to stay in business.
minimal least in amount or degree (adjective)
minimum the smallest possible number or amount (noun)

Examples  

Minimal editing will not result in a perfect paper.
You must buy a minimum of ten cases of Ding Dongs in order to get a discount.
minimal least in amount or degree (adjective)
nominal existing in name only; small, insignificant

Examples  

Queen Elizabeth II fills a nominal position; she has little to do with government.
I gave a nominal amount to the charity.
The store charged a minimal mark up on software hoping to sell hardware.