If not I think we might need a new term that can connotate (even if it takes time) the connecting line between two vertices. Line is good but it is very general and someone is going to try sneaking in their trivia about "m'actually it's a line segment", and those snowballing interruptions will never end whenever the topic comes up. Line segment also doesn't carry the connotation that it's connecting two vertices.
Edge doesn't really make sense to me. There are all kinds of edges and they're definitely not all line segments nor do they even have a sharp point to them, and I don't even know why else the word edge would be used.
Edge is very much correct, even if it's just an abstract graph drawn in 2D which doesn't represent a spatial polygon or polyhedron. Actually, there are a few very elegant proofs around which work by conflating graphs with polyhedra deliberately!
Normally in mathematics a Line means it extends infinitely in both directions, at least conceptually. Again, some geometric proofs need to allow this extension if their results are to hold everywhere successfully.
"Edge" is traditional. From Graph Theory: An Introductory Course by Béla Bollobás
A graph G is an ordered pair of disjoint sets (V, E) such that E is a subset of the set of unordered pairs of V. ... The set V is the set of vertices and E is the set of edges
There are two things to notice about that quote. First is the obvious point about the use of the word edge in a text book from 1979.
Second is the strange way that mathematicians write. They are careful to dodge saying more than they intend. Let me illustrate this with an example of a graph.
We might write V = {a, b, c} as the vertices of a graph with three vertices, a, b, and c. How many pairs of vertices are there? Nine. (a,a) (a,b) (a,c) (b,a) (b,b) ...
But the definition says unordered pairs. We throw out (a,a) and (b,b) We also consider (a,b) and (b,a) to name the same unordered pair. Not nine, but three unordered pairs: (a,b),(a,c),(b,c).
Also the definition says subset. For our example let us pick {(a,b),(b,c)}. We have an edge connecting a to b and a second edge connecting b to c, but we are missing the edge connecting a to c.
At this point one starts to notice the dodging. What is an edge? Somehow Béla Bollobás has avoided saying anything. We are clearly talking about a graph with three points, and vertex a connected to vertex b by an edge, but is an edge a line? A piece of string? The edge of a three dimensional polyhedron. Dodge, dodge, dodge. We just want to talk about which vertex is connected to which vertex, and calling the connection an edge fits in with English grammar and lets us write sentences that flow and look normal. We don't want an edge to mean anything more on top of that.
Dodge, dodge, dodge. We just want to talk about which vertex is connected to which vertex, and calling the connection an edge fits in with English grammar
Ok I get they're trying to be as abstract as possible and I've seen this writing before but when reading advanced math books (and thus in all-new territory) I instinctually question whether the writer meant to dodge ask that stuff and leave me on an abstract term. And I don't play guessing games like that soi throw away what I read. A prime example of why I don't play the guessing games is modern texting communication, especially with women. People expect for others to "the get point" through one to 3 word messages. Sometimes silence. There's no reason they can't be explicit here and get creative to come up with a proper word to leverage usage of the English language
that's better. i think i might have heard that used before too. have you seen that used in a textbook or class before? i wonder what else we can come up with.
Knowing how any word usage is going to shake out linguistically I have a feeling we're going to need a non-english word for people to draw a concept around. Edge has to go though if this topic is to be taught more efficiently.
[ + ] bosunmoon
[ - ] bosunmoon 0 points 3 monthsJan 8, 2024 19:30:57 ago (+0/-0)
[ + ] SithEmpire
[ - ] SithEmpire 1 point 4 monthsJan 2, 2024 21:19:56 ago (+1/-0)
Normally in mathematics a Line means it extends infinitely in both directions, at least conceptually. Again, some geometric proofs need to allow this extension if their results are to hold everywhere successfully.
[ + ] AugustineOfHippo2
[ - ] AugustineOfHippo2 1 point 4 monthsJan 2, 2024 20:49:14 ago (+1/-0)
[ + ] happytoes
[ - ] happytoes 0 points 4 monthsJan 3, 2024 09:22:00 ago (+0/-0)
There are two things to notice about that quote. First is the obvious point about the use of the word edge in a text book from 1979.
Second is the strange way that mathematicians write. They are careful to dodge saying more than they intend. Let me illustrate this with an example of a graph.
We might write V = {a, b, c} as the vertices of a graph with three vertices, a, b, and c. How many pairs of vertices are there? Nine. (a,a) (a,b) (a,c) (b,a) (b,b) ...
But the definition says unordered pairs. We throw out (a,a) and (b,b) We also consider (a,b) and (b,a) to name the same unordered pair. Not nine, but three unordered pairs: (a,b),(a,c),(b,c).
Also the definition says subset. For our example let us pick {(a,b),(b,c)}. We have an edge connecting a to b and a second edge connecting b to c, but we are missing the edge connecting a to c.
At this point one starts to notice the dodging. What is an edge? Somehow Béla Bollobás has avoided saying anything. We are clearly talking about a graph with three points, and vertex a connected to vertex b by an edge, but is an edge a line? A piece of string? The edge of a three dimensional polyhedron. Dodge, dodge, dodge. We just want to talk about which vertex is connected to which vertex, and calling the connection an edge fits in with English grammar and lets us write sentences that flow and look normal. We don't want an edge to mean anything more on top of that.
[ + ] iThinkiShitYourself
[ - ] iThinkiShitYourself [op] 0 points 4 monthsJan 3, 2024 19:45:49 ago (+0/-0)
Ok I get they're trying to be as abstract as possible and I've seen this writing before but when reading advanced math books (and thus in all-new territory) I instinctually question whether the writer meant to dodge ask that stuff and leave me on an abstract term. And I don't play guessing games like that soi throw away what I read. A prime example of why I don't play the guessing games is modern texting communication, especially with women. People expect for others to "the get point" through one to 3 word messages. Sometimes silence. There's no reason they can't be explicit here and get creative to come up with a proper word to leverage usage of the English language
[ + ]deleted
[ - ] deleted 0 points 4 monthsJan 3, 2024 00:41:55 ago (+0/-0)
[ + ] Cantaloupe
[ - ] Cantaloupe 0 points 4 monthsJan 2, 2024 23:48:51 ago (+0/-0)
7. the line along which two surfaces of a solid meet.
1. the outside limit of an object, area, or surface
• a willow tree at the water's edge
• she perched on the edge of a desk.
[ + ] MasterSuppressionTechnique
[ - ] MasterSuppressionTechnique 0 points 4 monthsJan 2, 2024 21:14:44 ago (+0/-0)
it's called a side
[ + ] chrimony
[ - ] chrimony 0 points 4 monthsJan 2, 2024 20:46:19 ago (+0/-0)
[ + ] iThinkiShitYourself
[ - ] iThinkiShitYourself [op] 0 points 4 monthsJan 3, 2024 00:02:40 ago (+0/-0)
Knowing how any word usage is going to shake out linguistically I have a feeling we're going to need a non-english word for people to draw a concept around. Edge has to go though if this topic is to be taught more efficiently.
[ + ] HonkyMcNiggerSpic
[ - ] HonkyMcNiggerSpic 0 points 4 monthsJan 2, 2024 20:14:45 ago (+0/-0)
[ + ] bosunmoon
[ - ] bosunmoon -1 points 4 monthsJan 2, 2024 20:10:59 ago (+0/-1)