Identically zero

  1. joshmccraney

    joshmccraney 525
    Gold Member

    hey pf!

    when would you use "identically zero" as opposed to simple "zero". example: f is identically zero on interval a to b. or, f is zero on interval a to b.

    why do we ever use identically? it seems superfluous...

    thanks!
     
  2. jcsd
  3. micromass

    micromass 18,677
    Staff Emeritus
    Science Advisor
    Education Advisor

    It's because the statement "##f## is zero on the interval ##[a,b]##", might be interpreted as there is a ##c\in [a,b]## such that ##f(c) = 0##. I know that the proper language should be that "##f## has a zero", rather than what I wrote. But writers want to be clear and write that it is identically zero to avoid misunderstandings.
     
    1 person likes this.
  4. SteamKing

    SteamKing 8,794
    Staff Emeritus
    Science Advisor
    Homework Helper

    'Identically' is sometimes used for emphasis.

    Of course, sin[itex]^{2}[/itex]θ + cos[itex]^{2}[/itex]θ is identically 1.
     
    1 person likes this.
  5. joshmccraney

    joshmccraney 525
    Gold Member

    thanks to you both!
     
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