I think the title is self explanatory, math people have often come up with misleading names which when literally taken carry a very different meaning to the actual mathematical definitions they represent. To defend these ambiguous nomenclatures, often the terms are initially coined in German, French or Russian and the literal translation have a slightly different meaning in English or maybe the people who coined them didn't care much for words, and just chose the first word that came to their mind to capture the abstract phenomenon. Take for example the term "uniform continuity", the powerseries $$ \sum_{k=1}^{\infty} z^{i} $$ indeed converges uniformly to $$\frac{z}{1-z}$$ on $$|z| \le .5$$. However this doesn't mean the series literally converges at an uniform rate everywhere, as the name would seem to suggest. At z=0, it converges instantly to zero, and as you go away it's tail dies ever more slowly.
To explain uniform continuity, suppose you are teaching a class calculus. Suppose the class has "countably" infinite students: Student 1,Student 2, Student 3, ....... . You can think of non convergence as the situation when there are people who will never be able to learn calculus. Convergence would be when everybody has the ability to learn calculus in some given time. However if you actually want to teach everyone calculus, this alone doesn't help you much. Suppose the ith student will learn calculus on the ith day. Given this situation, if you teach the class for N days (whatever be the N). Student N+1 onward will not have learnt Calculus. The analogue to what is mathematically called uniform continuity would be when not only every student can learn calculus, but there is a N, such that all students will have learnt calculus by the Nth day. For example , say student i learns calculus on min(i, 10) th day. Here by the 11th Day your job is done. This doesn't mean all the students learn calculus uniformly, the first student learns it on the very first day ahead of all else.
Anyway just writing random stuff on a Friday night, if you read enough math literature, you will grow accustomed with the mathematical meaning of terms and forget their English meaning while reading math. It's just sometimes a little confusing when people new to the subject read them. I doubt however the huge volume of mathematical literature can ever be revised to accommodate this problem, I think frankly it would be easier if the English dictionary was amended to solve the problem.
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