Bubble sort in pure CSS

Post by cubefox » Sun, Nov 05, 2023, 5:09 PM UTC

EGreg wrote: post #37

thaumasiotes wrote: post #18

Earlier quoted context omitted.

> It's called "addition" because you "add" another propostion, creating a disjunction. By that argument, conjunction is also called "addition". Perhaps there's a different reason? The choice of terminology, contrasting "logical addition" with "logical multiplication", obviously indicates that logical addition is supposed to be analogous to addition. What is the analogy?

The analogy is deep. But actually the relationship is as follows: P(A u B) = P(A) + P(B) - P(A^B) P(A ^ B) = P(A u B) - P(A) - P(B) And to the guy who said xor is addition — no it’s not: P(A xor B) = P(A) + P(B) - 2 * P(A^B) In Probability, when you have a space of outcomes, doing a Union on two disjoint events (sets of outcomes) the probabilities add. Whereas doing an Intersection on two non-disjoint events those pr…

Post by moritzwarhier » Sun, Nov 05, 2023, 5:19 PM UTC

cubefox wrote: post #50

moritzwarhier wrote: post #39

Earlier quoted context omitted.

This is the obvious solution I was looking for. Thanks! (and I rightfully feel stupid now)

The formula is slightly wrong though. This is the right one: a or b = a + b - (a * b) The last term is equivalent to a conjunction. Which also makes sense when you think of probability: P(a or b) = P(a) + P(b) - P(a and b)

Post by cubefox » Sun, Nov 05, 2023, 5:45 PM UTC

thaumasiotes wrote: post #18

dvt wrote: post #16

Earlier quoted context omitted.

It's called logical addition which is different than arithmetic addition, so it's best to not conflate the two. It's called "addition" because you "add" another propostion, creating a disjunction. And by the rules of logic, as long as the original proposition was true, the truth value is preserved no matter how many propositions you introduce (or "add"). A ⊢ ((A ∨ B) ∨ C) ... ∨ n

> It's called "addition" because you "add" another propostion, creating a disjunction. By that argument, conjunction is also called "addition". Perhaps there's a different reason? The choice of terminology, contrasting "logical addition" with "logical multiplication", obviously indicates that logical addition is supposed to be analogous to addition. What is the analogy?

Post by pzmarzly » Sun, Nov 05, 2023, 6:01 PM UTC

pzmarzly wrote: post #5

> (oneIsGreater * origArray[0]) + (twoIsGreater * origArray[1]) There is a reason why conjunction (AND) is also called logical multiplication, and disjunction (OR) logical addition. There is not much difference between this and: (oneIsGreater ? origArray[0] : 0) | (twoIsGreater ? origArray[1] : 0) This is often useful to think about when working on bitset or SIMD algorithms.

Post by cubefox » Sun, Nov 05, 2023, 6:19 PM UTC

adrian_b wrote: post #40

moritzwarhier wrote: post #34

Earlier quoted context omitted.

That makes sense, thank you for your great reply. As someone without much mathematical ropes, this might also be related to non-integer algebra and the distinction of "smooth" (edit: or differentiable) and discontinuous functions, no? > The functions maximum and minimum are arithmetic functions as important as addition and subtraction. The only reason for which they have not been counted among the basic arithmetic fu…

As I have mentioned, in the logic systems with 3 or more discrete values of truth (e.g. false, unknown and true, or false, unlikely, unknown, likely and true) and also in the logic systems with a continuous range of truth values (e.g. those based on probabilities), to the base logic functions AND, OR and NOT, correspond the base logic functions minimum, maximum and inversion a.k.a. reflection functions (the last may…