The quality or state of not being breakable.(noun)
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Use "unbreakableness" in a sentence
"She had been buggy-riding before, but always behind one horse, jaded, and livery, in a top-buggy, heavy and dingy, such as livery stables rent because of sturdy unbreakableness."
""Another thing that pleases me," continued my lady, "is the unbreakableness of the dishes."