Without a bath or bathing facilities; lacking the ability or opportunity to bathe.
From 'bath' (Old English 'bæð') plus the negating suffix '-less' (Old English '-lēas'). This compound form follows standard English word formation patterns to indicate absence or lack.
In historical contexts, being 'bathless' was actually common—most peasants lived their entire lives without bathing facilities, using rivers instead, which is why cities became dangerously unsanitary.
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