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Identically zero

  1. May 25, 2014 #1

    joshmccraney

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    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. May 25, 2014 #2

    micromass

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    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.
     
  4. May 25, 2014 #3

    SteamKing

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    'Identically' is sometimes used for emphasis.

    Of course, sin[itex]^{2}[/itex]θ + cos[itex]^{2}[/itex]θ is identically 1.
     
  5. May 26, 2014 #4

    joshmccraney

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    thanks to you both!
     
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