Talk:Q17020770

codomain=bool

@Andreasmperu: sorry, I don't understand what is more in Q20820264 and Q17020770 than codomain. So I presume they are basically the same. Infovarius (talk) 15:23, 13 October 2022 (UTC)

I would say that logical operator (Q20820264) is a subclass of Boolean-valued function (Q17020770). Boolean-valued function (Q17020770) may have a non-Boolean domain (e.g. equals(123, 456) = 0). --Horcrux (talk) 09:44, 14 October 2022 (UTC)

I withdraw what I said: logical values are not only Boolean, we have also many-valued logic (Q185502). --Horcrux (talk) 09:15, 17 October 2022 (UTC)

Integer codomain?

@Infovarius: I don’t think Boolean-valued function (Q17020770) is a integer-valued function (Q19856468). It’s a function to Boolean domain (Q3269980) which might be (often) written/modeled as specifically $\{0,1\}$, but it’s not really the set of those two integers; it’s just any two-element set where the elements represent “true” and “false”, truth value (Q185521) (or “a member of the set”, “not a member of the set”, etc.). See e.g. MathWorld. Mormegil (talk) 16:28, 3 January 2024 (UTC)

Hi, Mormegil, I had the same thoughts when I made this edit actually. But what is "integer"? It is just a model too (and 2 of them can be represented as "true" or "false"...). --Infovarius (talk) 22:06, 4 January 2024 (UTC)

I don't fully agree with the interpretation given by Infovarius. We can also model Boolean domain (Q3269980) using $\{{\sqrt {1}},{\sqrt {-1}}\}$, or $\{{\sqrt {1}},{\sqrt {2}}\}$ or $\{\triangle ,\bigtriangledown \}$. In all these cases the function would not be a integer-valued function (Q19856468). --Horcrux (talk) 10:23, 5 January 2024 (UTC)

Oh, I don’t know about that. That would mean countable set (Q66707394) should be a subclass (?!?) of set of integers (Q47007735) (any countable set could be modeled with the naturals)? Nah, I don’t think so. Boolean domain (Q3269980) is a subclass of finite set (Q272404), not of set of integers (Q47007735). We might have e.g. a “function into a finite set” class (with codomain (P1571)finite set (Q272404)) and use that as the superclass here but “integer function”? No, that’s depending on just one specific interpretation instead of using a general statement. --Mormegil (talk) 08:34, 8 January 2024 (UTC)

Ok, you both have fully convinced me. --Infovarius (talk) 10:14, 10 January 2024 (UTC)