# Identically zero

1. ### joshmccraney

600
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. ### micromass

19,788
Staff Emeritus
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.
3. ### SteamKing

10,305
Staff Emeritus
'Identically' is sometimes used for emphasis.

Of course, sin$^{2}$θ + cos$^{2}$θ is identically 1.

1 person likes this.
4. ### joshmccraney

600
thanks to you both!