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Identically zeroby joshmccraney
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#1
May2514, 03:48 PM

P: 320

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
May2514, 04:04 PM

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P: 18,036

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.



#3
May2514, 10:27 PM

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PF Gold
P: 6,305

'Identically' is sometimes used for emphasis.
Of course, sin[itex]^{2}[/itex]θ + cos[itex]^{2}[/itex]θ is identically 1. 


#4
May2614, 09:31 PM

P: 320

Identically zero
thanks to you both!



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