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Identically zero

by joshmccraney
Tags: identically
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May25-14, 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...

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May25-14, 04:04 PM
micromass's Avatar
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.
May25-14, 10:27 PM
Sci Advisor
HW Helper
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.

May26-14, 09:31 PM
P: 320
Identically zero

thanks to you both!

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