About the word “limit” used in calculus

In the introduction of the limits chapter of a scholar book I can read (translated and abstract) the following examples:

1. "the price of a product has a limit value that, from this price, the number of sales start to decrease, reducing the benefits"
2. "the light speed has a limit"
3. "the population of animals is limited due to the amount of food"

For me, these examples are not correct examples of a limit in the sense used in calculus: 1 and 3 are a function maximum, example 1 is a maximum of the function f:price->benefit and example 2 is a empirical maximum, base of the special relativity theory (I do not known any formula that gives light speed as root, maximum or limit of an expression ).

It is true that in a lot of situations in normal life, limit and maximum are synonyms. But not in math.

Thus, I wonder if in the classroom we must strengthen the usage of words as "tendency", "trend", ... even when in the written math expression still using $$\lim$$.

• I would continue to use the word limit in math class normally. 99% approaching asymptotically (haha) of these suggestions for changes in the traditional terminology and coverage are bad ideas. And they generally do NOT represent observed difficulties by the students but instead fussy observations of the instructor (often a TA or newish professor). – guest Nov 2 at 13:11
• I agree with part of @guest's comment; I don't think you can change the terminology "limit". But I don't think your concerns are merely fussy. Students (in the U.S.) are certainly familiar with the phrase "speed limit" and probably with phrases like "limit of his endurance" or "limit of his patience", in which "limit" means maximum. So this dissonance between the mathematical meaning and other meanings of "limit" deserves to be discussed in class. – Andreas Blass Nov 2 at 13:25
• @guest: thanks for your comment. 3 of 3 wrong examples in a book (if my rationale is correct) points to something deeper than a fussy observation. – pasaba por aqui Nov 2 at 13:37
• @AndreasBlass: in fact, when we read "f(x)->4 when x->5" we say "tiende a" ("trends to" in english ?) not "limita con" ("limits with") – pasaba por aqui Nov 2 at 13:42
• It's also correct in English to say "f(x) tends to 4 when x tends to 5" but it's more common to say "approaches" rather than "tends to". The real difficulty arises when you need a noun, as in "the limit of f(x) as x approaches 5"; I don't think there's any standard substitute for "limit" in this context. – Andreas Blass Nov 2 at 13:45