The word "continuousnesses" is quite a mouthful, but it essentially means the state of being continuous or uninterrupted. Thankfully, there are a number of synonyms that can be used instead. These include continuity, constancy, regularity, persistency, endurance, and perpetuity. Each of these words conveys the sense of something that is ongoing, unbroken, and consistent. Someone might use these synonyms when talking about the continuousnesses of a river's flow, the constancy of a lover's devotion, or the perpetuity of a family's traditions. No matter which synonym is chosen, the overall meaning of the sentence will remain the same - something that is continuous and unceasing.