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