Difference between revisions of "Talk:Additive function"
From Maths
m |
(sure) |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 4: | Line 4: | ||
: 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 {{M|f:X\rightarrow Y}} with the property that {{M|1=f(a+_Xb)=f(a)+_Yf(b)}} for whatever addition meant in {{M|X}} and {{M|Y}}. | : 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 {{M|f:X\rightarrow Y}} with the property that {{M|1=f(a+_Xb)=f(a)+_Yf(b)}} for whatever addition meant in {{M|X}} and {{M|Y}}. | ||
: 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. [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 22:45, 19 March 2016 (UTC) | : 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. [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 22:45, 19 March 2016 (UTC) | ||
| + | |||
| + | :: Oops, now "'''Claim 1: ''' {{M|f}} is finitely additive {{M|\iff}} it is additive" is generally wrong. Take a finite set {1,2,3}, and {{M|\mathcal{A} }} 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. [[User:Boris|Boris]] ([[User talk:Boris|talk]]) 12:31, 20 March 2016 (UTC) | ||
| + | ::: I'll tell myself I would have discovered that when writing the proof for the claim ;-) [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 16:14, 20 March 2016 (UTC) | ||
| + | :::: Sure. Anyway, when generalizing usual definitions, do fear to face the consequences. [[User:Boris|Boris]] ([[User talk:Boris|talk]]) 18:11, 20 March 2016 (UTC) | ||
Latest revision as of 18:11, 20 March 2016
"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)
