pointedset

3 ms·

1. 1.▲
   by pointedset 4y ago

   I think your quote from Gallian doesn't address syzarian's example, actually. The two properties you quoted are about the fact the distributivity works whether you're multiplying on the left or on the right. That's one p
2. 2.▲
   by pointedset 4y ago

   Note that for this property, you want edges to be reasonably close, but you also need to say that vertices are reasonably far apart: otherwise you could always get a "less tangled" graph by just shrinking it until it's too sm
3. 3.▲
   by pointedset 4y ago

   Yes, if "untangled" means "no edge crossings", then 3 dimensions is enough for any graph to be untangled. As a proof, you can put the vertices at coordinates (0, 0, 0), (1, 1, 1), (2, 4, 8), (3, 9, 27), ..., (n, n^2, n^3
4. 4.▲
   by pointedset 5y ago

   Unfortunately, constructive vs classical (vs linear, etc.) applies to proofs, but this is really about definitions. Proofs can be correct or incorrect pretty straightforwardly, but definitions being correct or not is really a matter of tast
5. 5.▲
   by pointedset 5y ago

   Now you're reminding me of a wacky math conversation I had at Mathcamp [1] with a much smarter guy, who was talking about more esoteric definitions of volume in euclidean space. Something like: - n-dimensional volume is a function from
6. 6.▲
   by pointedset 5y ago

   Yes, those two facts about zero/empty cases (and so many more) are definitely related, and this class of facts is one of my favourites! Usually, if you're dealing with something algebraic in flavour (which is a very vague concept,