[{"data":1,"prerenderedAt":134},["ShallowReactive",2],{"word-monotonically":3},{"source":4,"data":5,"quality_score":132,"lastmod":133},"static_word_details",{"lemma":6,"phonetic":7,"pos":9,"definition_zh":11,"usage_points":12,"collocations":34,"examples_basic":90,"examples_advanced":100,"common_mistakes":110,"synonyms_nuance":119,"diff_pairs":128,"word_family":131},"monotonically",{"us":8,"uk":8},"mɒnə'tɒnɪklɪ",[10],"代词","单调地，指以恒定不变或持续增加/减少的方式，常用于描述数学函数、数据趋势或重复性行为。",[13,20,27],{"title":14,"content":15,"examples":16},"句型搭配","通常用于修饰动词，描述动作或状态以单调方式变化，常见于数学、统计、计算机科学等领域，表示持续增加或减少。",[17,18,19],"increase monotonically","decrease monotonically","behave monotonically",{"title":21,"content":22,"examples":23},"介词用法","常与介词“with”或“in”连用，表示随某个变量单调变化，例如“monotonically with time”表示随时间单调变化。",[24,25,26],"monotonically with time","monotonically in value","monotonically over the range",{"title":28,"content":29,"examples":30},"语域说明","主要用于正式或学术语境，如数学、工程、经济学，较少用于日常口语，在非正式对话中可用“steadily”或“consistently”替代。",[31,32,33],"monotonically increasing function","monotonically convergent sequence","monotonically related variables",[35,46,56,67,75,83],{"type":36,"items":37},"verb",[38,39,40,41,42,43,44,45],"increase","decrease","rise","fall","grow","decline","change","vary",{"type":47,"items":48},"adjective",[49,50,51,52,53,54,55],"monotonic","increasing","decreasing","constant","steady","linear","non-decreasing",{"type":57,"items":58},"noun",[59,60,61,62,63,64,65,66],"function","sequence","trend","relationship","curve","data","series","behavior",{"type":68,"items":69},"adverb",[70,71,72,73,74],"strictly","almost","approximately","generally","typically",{"type":76,"items":77},"preposition",[78,79,80,81,82],"with","in","over","across","throughout",{"type":84,"items":85},"phrase",[31,86,87,88,89],"monotonically decreasing trend","monotonically with respect to","monotonically over time","monotonically convergent",[91,94,97],{"en":92,"zh":93},"The temperature increased monotonically throughout the day, making it feel very hot.","温度在一天中单调上升，让人感觉很热。",{"en":95,"zh":96},"Her voice sounded monotonically during the long lecture, so some students got bored.","她在漫长的讲座中声音单调，所以有些学生感到无聊。",{"en":98,"zh":99},"The stock price has been falling monotonically for weeks, worrying investors.","股价几周来单调下跌，让投资者担忧。",[101,104,107],{"en":102,"zh":103},"In calculus, a function is said to be monotonically increasing if its derivative is non-negative over an interval.","在微积分中，如果一个函数在某个区间内导数非负，则称其为单调递增函数。",{"en":105,"zh":106},"The algorithm ensures that the error decreases monotonically with each iteration, guaranteeing convergence.","该算法确保误差在每次迭代中单调减少，从而保证收敛性。",{"en":108,"zh":109},"Economic models often assume that utility increases monotonically with income, though this may not always hold in reality.","经济模型通常假设效用随收入单调增加，尽管这在现实中不一定成立。",[111,115],{"wrong":112,"right":113,"explanation":114},"The music played monotonically, so I enjoyed it.","The music played monotonically, so I found it boring.","错误在于逻辑矛盾：'monotonically' 通常表示单调乏味，与 'enjoyed' 冲突。应改为 'found it boring' 以匹配语境。",{"wrong":116,"right":117,"explanation":118},"He speaks monotonically in a lively way.","He speaks in a lively way, not monotonically.","错误在于用词矛盾：'monotonically' 和 'lively' 意义相反，不能同时修饰。应分开表达或使用否定结构。",[120,124],{"word":121,"difference":122,"example":123},"steadily","'steadily' 强调稳定、持续不变，但可能包含轻微波动；而 'monotonically' 更精确地表示数学或逻辑上的单调性，常指严格增加或减少。","The population grew steadily over the decade. (稳定增长，可能有起伏) vs. The function increases monotonically. (严格单调递增，无下降)",{"word":125,"difference":126,"example":127},"consistently","'consistently' 侧重行为或结果的一贯性、可靠性；'monotonically' 则强调变化模式的单调性，常用于技术语境描述趋势。","She consistently performs well in exams. (一贯表现好) vs. The data shows a monotonically decreasing trend. (数据呈现单调下降趋势)",[49,129,130],"monotonous","monotone",[],70,"2026-01-09T00:06:25.041Z",1781752504673]