Talk:Additive function

"Warning about structure": "[math]\dots\implies f(0)=0[/math] so one must be careful!" --- I do not get the hint; naturally, additive function between groups sends 0 into 0, but why one must be careful? Boris (talk) 07:59, 19 March 2016 (UTC)

"On set functions": "for valued set functions (set functions that map to values)" --- ?? What is meant by "values"? I know what is called the value of a function; but is there a notion of a function that maps something to non-values?? Boris (talk) 08:03, 19 March 2016 (UTC)

At the time (I think, it was a year ago and I was using this as a notebook back then!) I think what happened was I thought "additive function" should mean any function that preserve addition. So a map [ilmath]f:X\rightarrow Y[/ilmath] with the property that [ilmath]f(a+_Xb)=f(a)+_Yf(b)[/ilmath] for whatever addition meant in [ilmath]X[/ilmath] and [ilmath]Y[/ilmath].

I think I am warning that it may not be true for all structures. However I cannot think of a counter-example right now; either way I've updated the page. I do want to move set functions to their own page though. Alec (talk) 22:45, 19 March 2016 (UTC)

Oops, now "Claim 1: [ilmath]f[/ilmath] is finitely additive [ilmath]\iff[/ilmath] it is additive" is generally wrong. Take a finite set {1,2,3}, and [ilmath]\mathcal{A} [/ilmath] containing the three singletons (one-point sets) and the whole {1,2,3}, but no two-point sets. Here additivity is void, but finite additivity is not. Boris (talk) 12:31, 20 March 2016 (UTC)

I'll tell myself I would have discovered that when writing the proof for the claim ;-) Alec (talk) 16:14, 20 March 2016 (UTC)

Sure. Anyway, when generalizing usual definitions, do fear to face the consequences. Boris (talk) 18:11, 20 March 2016 (UTC)