The quality or state of having no gaps or breaks; the condition of being continuous and complete.
From 'gapless' plus the nominalizing suffix '-ness' (from Old English, meaning 'quality or state'). This creates an abstract noun describing the condition itself rather than something that possesses it.
While 'gapless' is common in tech, you almost never hear 'gaplessness' spoken aloud—it's the kind of word that makes perfect logical sense but sounds awkward, which is why English prefers 'continuity' in actual conversation.
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