monotonically
用法要点
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。
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。
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。
基础例句
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。
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。
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。
高级例句
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。
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。
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。
高频搭配
verb
adjective
noun
adverb
preposition
phrase
常见错误
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。
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。
近义词辨析
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)
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)