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Thread: [SOLVED] Vocabulary question

  1. #1
    MHF Contributor

    Aug 2008
    Paris, France

    [SOLVED] Vocabulary question


    I was wondering how you would read (in plain English) a formula like the following one: $\displaystyle \sin x\underset{x\to0}{\sim}x.$
    (which is equivalent to writing $\displaystyle \sin x=x+\underset{x\to 0}{o}(x)$ or $\displaystyle \lim_{x\to 0, x\neq 0}\frac{\sin x}{x}= 1$)

    I would be inclined to say "sine of x is equivalent to x as x tends to zero" (mimicking the French expression), but I can't find any reference to such "equivalence" (?) of functions (or sequences) in English on the internet (even in online textbooks).

    This topic is covered during the first year in french universities, and much emphasis is given to this equivalence relation as a tool to compute limits or study the convergence of a series or of an improper integral. Of course it can be avoided using the "little o" relation, and this is why I wondered if English or American maths students hear about it.

    I wish someone can answer me... Any piece of information will be wellcome. Thanks in advance.

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  2. #2
    Super Member wingless's Avatar
    Dec 2007
    It's called "asymptotic equivalence".

    See Asymptotic analysis - Wikipedia, the free encyclopedia
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