Identically zero

1. May 25, 2014

joshmccraney

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. May 25, 2014

micromass

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.

3. May 25, 2014

SteamKing

Staff Emeritus
'Identically' is sometimes used for emphasis.

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

4. May 26, 2014

joshmccraney

thanks to you both!