Firm means solid, steady, and not easily pressed down or changed. As a noun, it can also mean a business organization, especially a company of professionals.
It comes from Latin “firmus,” meaning “strong” or “stable,” through Old French into English. The business sense grew from the idea of a stable, established enterprise.
“Firm” connects physical solidity (a firm mattress) with mental and social solidity (a firm decision, a firm). The same root built “affirm” and “confirm,” all about making things feel more solid and sure.
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