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seen Sep 9 at 0:14

Feb
28
comment How to pronounce $\setminus$
But is that the way you in practice pronounce it?
Feb
28
comment “Binomial theorem”-like identities
@anon: falling factorials are counting (iteratively) selection without replacement (and rising factorials do the same starting from the top).
Feb
25
asked Connecting finite automata and regular languages in teaching/applications
Feb
13
comment Category of Trees as sub-category of Category of Graphs
@DamianSobota: you could make that a full answer rather than a comment.
Dec
4
comment A list of all algebras?
Here's a WP list of algebras.
Oct
31
comment New to probability - Is this true?
20-sided die (and also 12-sided die) are notoriously non-random. Because the angles at the vertices and edges are so obtuse, even without deliberate modification, they are very easy to wear to the point where some sides are favored rather than others. A better physical device to get 1 through 12 would be to roll a 6-sided side and flip a coin: add 6 for tails and 0 for heads. But of course theoretically, leaving out 13 through 20 works just fine.
Oct
22
answered If both $P$ and $Q$ are true , how can I tell that $P$ implies $Q$?
Oct
17
comment How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
@Mariano: Re: not counting NNx or C(x)(tautology) - you might be able to syntactically ignore the latter (if you enumerate a system that includes enumerating tautologies, but eliminating double negation seems hard (just intractable to create the system of equations). Anyway, might as well include those because those are viable tautologies.
Oct
17
revised How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
brief extra explanation
Oct
17
comment How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
@Mariano: sorry, it was typed on an iPhone..somehow hard to think in a really tiny screen! I'll try to embellish my answer to help explain.
Oct
17
comment How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
@Mariano: oh duh... but easy to miss.
Oct
17
comment How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
Above you say you get 290 for 8 vars, but in the sequence at the bottom you give 198. Which is it?
Oct
17
comment How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
@Doug: I only considered 2 variables because, well, I mistakenly read too fast (you mentioned the number '2') and because it's crazy complicated with more anyway. So then I'll take Mariano's advice as the real justification. Anyway, you'd probably want to parameterize your exploration by number of variables anyway...oh yeah and also the set of operators ({AND, NOT}, {AND, OR, NOT}, {AND, OR, NOT, IMPLIES}, {NAND}, etc...)
Oct
17
comment How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
@Mariano: it's context-free but not regular, for any number of variables. Infix or prefix doesn't matter - see my answer.
Oct
17
revised How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
extra explanation
Oct
17
comment How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
@Doug: just stick with two variables, letters x and y, as a first thing to compute. What are all the ways of getting a particular Boolean function using C, N, p, and q, if all you're doing is adding one operator? You have to check how -any- Boolean function could be reached by the two operators (when only two vars allowed).
Oct
17
answered How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
Oct
17
comment How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters?
Generate and test? That is, write a program to generate all possible wffs, and then do a truth table on each one.
Oct
16
comment Least-effort way from A to B via X
What have you tried so far?
Oct
5
comment On the automated solution of Olympiad problems
I think you just identified the difficulty in automated theorem proving: all mathematical research is devoted to solving problems in a definitive manner. And this is ostensibly automatable, except research papers are difficult to formalize, and even informal everyday -word- problems are difficult to translate to symbolism, at least automatically.