Without interruption or break; in an unbroken sequence or flow.
Also from Latin 'continuus,' but emphasizing the unbroken aspect more strictly than 'continually.' The distinction between the two words became more pronounced in modern English as speakers needed to differentiate between interrupted and uninterrupted ongoing action.
The word 'continuously' is like a linguistic straight line - it tolerates no breaks, gaps, or pauses. In mathematics and science, this precision matters enormously, which is why continuous functions and continuous variables are fundamental concepts that require this exact meaning.
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