| 13 Nov 2020 |
 VIVIT | Oh hold on. | 22:07:06 |
 Cur_固嚛訥 | * {2, 2, 2, 2, 3, 3, 5} | 22:08:58 |
| Cur_固嚛訥 | (I missed a 2 in that set) | 22:09:55 |
| VIVIT | By "factor into primes" mean "factor a number all the way out into an expression containing each of its prime factors" (factoring 42 into 2×3×7, for example). I thought you meant "be a factor of primes" the same way that 2, 3, and 7 each factor into 42. | 22:10:45 |
| Cur_固嚛訥 | LOLO yes | 22:11:03 |
| VIVIT | Also what you have there isn't quite a set; it's a multiset. | 22:11:30 |
| Cur_固嚛訥 | The depends on how I've classed the set which I've provided you with : p | 22:12:35 |
| VIVIT | A plain old set cannot have more than one of the same element: {a, b, c} is a set, but {a, a, b, c} is a multiset. | 22:13:31 |
| Cur_固嚛訥 | oh | 22:13:51 |
| Cur_固嚛訥 | Seems counter-intuitive to make an exclusionary set the default. Especially since the vernacular has popular incongruent usage. | 22:16:52 |
| VIVIT | A set is a collection of zero or more unique things. If you have more than one of the same thing in that set, that thing is no longer unique, and the set isn't a set. | 22:17:08 |
| VIVIT | Yeah, mathematical English is very different from vernacular English. | 22:18:16 |
| Cur_固嚛訥 | Why even make that distinction though? Other than a mathematician making their preferences clear lol. | 22:19:30 |
| VIVIT | It's useful to make exclusionary sets the default because it's common to talk about things like "the set of all integers" or "the set of all prime numbers", and it would be annoying to have to always specify "the set that contains one unique instance of every integer". | 22:20:36 |
| VIVIT | Oh, it's a very important distinction. The rules are different, so the mathematical truths you're dealing with are different. | 22:21:11 |
| VIVIT | "Chess except pawns can move two squares forward whenever they want" is a very different game from normal chess, streatgeically speaking, even though it's not that big of a change to the rules. | 22:24:23 |
| VIVIT | * "Chess except pawns can move two squares forward whenever they want" is a very different game from normal chess, strategically speaking, even though it's not that big of a change to the rules. | 22:24:36 |
| Cur_固嚛訥 | I'll reserve my skepticism. | 22:26:21 |
| VIVIT | If you wanted to work with multisets only, you could say, "By 'set' I mean multiset" and stick with that definition, but it would be confusing to everyone who's used to the conventional definition. | 22:26:23 |
| VIVIT | Another, IMO quite amusing word for "multiset" is "bag". | 22:27:20 |
| VIVIT | Multisets are more complicated then sets because in a multiset, every element has an additional property to keep track of: its multiplicity; i.e. how of that element you have. In the multiset {a, a, b}, a has a multiplicity of 2 and b has a multiplicity of 1. | 22:30:55 |
| VIVIT | In a normal set, the idea of multiplicity is irrelevant. | 22:31:50 |
| Cur_固嚛訥 | Makes sense, though not very portable with computer science. | 22:33:50 |
| VIVIT | It also makes the definitions of other ideas more complicated. The magnitude of a set is the number of elements. The magnitude of a multiset is the sum of the multiplicities of all unique elements. | 22:36:24 |
| Cur_固嚛訥 | I would prefer to say size lol | 22:37:16 |
| VIVIT | Magnitude is more specific. | 22:38:28 |
| Cur_固嚛訥 | or perhaps amount of entropy.. | 22:38:46 |
| Cur_固嚛訥 | Yeah, you got me there. | 22:39:02 |
| VIVIT | Would you talk about the "size" of a line? | 22:45:13 |
| VIVIT | No, you'd talk about its length. | 22:45:18 |
