Talk:Q44946

subclass of (P279) zero-dimensional space (Q1801244)

@Infovarius: I initially removed the statement linking this item to zero-dimensional space (Q1801244) because it seems to me that this item is mostly used as a philosophical concept rather than a mathematical one. What bothers me with this statement is that if we keep it, then any geographical feature (Q618123) becomes an instance of a zero-dimensional space (Q1801244) (and therefore all its ancestors, such as completely regular space (Q1191433)). For instance, if we keep this statement, any garden (Q1107656) is a zero-dimensional space (Q1801244) (see the graph). I understand that, when considering a garden as a point in space, we can indeed see it as a zero-dimensional space, but that is quite awkward.

If you are only worried about mathematical correctness, consider this case: currently a border (Q133346) is a zero-dimensional space (Q1801244). I think that the common sense would rather indicate that it is a one-dimensional space. I guess physicists would argue that if you look from far enough, everything becomes a point, but I am not sure we want that in the ontology!

A mathematician friend pointed out to me that the issue comes from the confusion between an element (the point) and the singleton it defines (the one-point set which is indeed zero-dimensional). Mathematically these are different objects! This is the reason why this subclass of (P279) link seems to be the best one to remove in the chain.

But I am happy to keep this statement if we remove another one in the chain from geographical feature (Q618123) to zero-dimensional space (Q1801244). Or maybe I'm asking for too much correctness and nothing really makes sense when you follow subclass of (P279) too many times? − Pintoch (talk) 18:37, 13 March 2017 (UTC)

@Infovarius: Do you agree with the above? If so, I'll remove the statement again. Cheers. − Pintoch (talk) 20:59, 17 March 2017 (UTC)

@Pintoch:, thanks for the analysis. Indeed there's a problem in "subclass" tree. I suppose it can be in a chain "position -> point", I'll try to remove that. --Infovarius (talk) 18:07, 18 March 2017 (UTC)

@Infovarius: I really think the claim I removed is really the faulty one: a point is simply not a zero-dimensional space. A set containing a single point is. What's wrong with position -> point for you? − Pintoch (talk) 22:28, 18 March 2017 (UTC)

@Pintoch: 1) what does contain a set besides a point? 2) I am not sure, but position (location) can also include elongated objects. Infovarius (talk) 02:54, 20 March 2017 (UTC)

@Infovarius: The element $x$ and the set $\{x\}$ are different mathematical objects. For instance, in set theory you can define the natural numbers as follows: $0=\emptyset$ (the empty set), $1=\{\emptyset \}$ (the one-element set whose only element is the empty set), $2=\{\emptyset ,\{\emptyset \}\}$, and so on (see en:Set-theoretic definition of natural numbers). As you can see, in this construction it is crucial that $\emptyset \neq \{\emptyset \}$, otherwise we would have $0=1$! So, saying that the point $p$ and the zero-dimensional space $\{p\}$ are equal is just wrong. − Pintoch (talk) 09:38, 20 March 2017 (UTC)

relation to line(s)

Line can be defined using 2 points or via matrix or via coefficients, so we must have 3 items at least

We can only claim produced from matrix or from two (n) points using specific items.

English Wikipedia mentions lines in geometry-other-than-Euclidean. This is another separation.

@Fractaler: d1g (talk) 06:39, 23 September 2017 (UTC)

@D1gggg: matrix (Q44337): rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Point is a geometric analog (~) of a number (next: line ~ series (group) of numbers, etc.) --Fractaler (talk) 12:41, 24 September 2017 (UTC)

My bad confused line (Q1228250) with line (Q37105) - both are lines. d1g (talk) 16:31, 26 September 2017 (UTC)