What is the Difference Between 'Identically Zero' and 'Zero' in Mathematics?

[member 428835]

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!

 

[micromass]

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.

 

[SteamKing]

'Identically' is sometimes used for emphasis.

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

 

[member 428835]

thanks to you both!