Mathematical idempotency depends heavily on the function's domain. It's not too challenging to construct a non-idempotent function that has an idempotent restriction. So depending on what your domain of interest some operations may be idempotent or not.

In the hello world example, I guess we are considering 'echo' as the function. If then if we consider stdout and echo's args to be the same, echo will be idempotent.

However, stdout and command args are pretty different things on any system I know. If we care about things like command line history, then clearly 'echo hello world' is not idempotent.

I disagree that your ‘ echo hello’ example is free of side effects. It writes to stdout. It overwrites $?. It changes the value of the last executed history command. Etc.

About the only side effect free operation at a blank line terminal prompt is _probably_ hitting enter or ctrl c. Or ‘#something<Enter>’

But your idempotency examples are spot on.

Basically, idempotency is a very useful concept. Side effect free isn’t.

Interestingly, in this case the non-idempotent option is less safe.

You're right, I meant to summarize more along the lines that calling something multiple times doesn't cause more than one set of side effects. Unfortunately too late to edit by the time I re-read it!