Being the greatest or highest possible; relating to or being a maximum value or extent.
From Latin maximus meaning 'greatest,' with the adjectival suffix -al. The mathematical and scientific usage developed in the 19th century as precision in measurement and optimization became more important.
In mathematics, a maximal element in a set isn't necessarily the largest overall - it's just an element that can't be exceeded within that particular set, a subtle but crucial distinction in advanced mathematics.
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