On 19 August 2013 19:26, Keshav Kini <keshav.k...@gmail.com> wrote: > John Cremona <john.crem...@gmail.com> writes: >> [...] and then you will not have the silly >> situation that (in 5.11) >> >> sage: G = Graph([]); G >> Graph on 0 vertices >> sage: G.is_connected() >> True >> sage: G.connected_components() >> [] >> as to me it seems contradictory to have a graph claiming to be >> connected but having no connected components. > > Why? A graph is connected iff every pair of vertices is connected, which > is to say that every connected component is the same as every other > connected component (i.e. a uniqueness property). The existence of a > connected component seems to me to be independent from the uniqueness of > a connected component, and so either 0 or 1 connected components should > be admitted. >
I was trying to argue against any position based on " my favourite definition is ... and it satisfies that definition" since the whole point is that there are many different defintions which agree on nontrivial cases but give different result for the trivial cases. If you define a prime number to be an integer with precisely 2 prime divisors, itself and 1, then you find that the only prime number is -1. It seems (to me) much better to decide on an important property which you want to be true -- such as uniqueness of primes factorizations, or decompositions into connected components, and use the definition for trivial objects which is consistent with that. John > Anyway, I'm not trying to argue that the empty graph should be > considered connected. Maybe it is more useful to define connectedness by > existence *and uniqueness* of connected components, after all. I like > the nLab wiki link that darij provided in the ticket description [1]. > I'm especially tickled by the example, "False is not true" :) > > -Keshav > > [1] http://ncatlab.org/nlab/show/too+simple+to+be+simple > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
