I don’t quite get the difference between “any” and “every” (in the more interesting cases.) Does “every 2 out of 30 [things have this property]” mean the set of ordered twos as a whole thing (unlike “any 2 two out of 30″, which is talking about any one combination of two things but not all possible combinations taken at once?
And if “every” needs some kind of order, even if we don’t know which, and some kind of “presented-togetherness”, then we can, for example, say, “[every two out of four] out of [every thirty out of thirty]”, but I don’t quite understand what it would say...
I mean, it doesn’t have to be something trivial like “every apple out of thirty apples has a spot on its side”, it can be something like “every node out of thirty is connected to another node”. But even this second case does not quite fit. Are there even objects for which “every 2 out of 30” and “every 1 out of 30″ are two distinct things?
“For every x, property(x) holds” means “it is not the case that for any x, property(x) does not hold.”
“For any x, property(x) holds” means “it is not the case that for every x, property(x) does not hold.”
In Russian, quantifier adjectives are often implicit, which could be a part of the problem here. Native Russian speakers (like me) often have problems with this, also with definite vs indefinite articles in English.
edit: not only implicit but ambiguous when explicit, too!
Person below is right, “every” is sort of like an infinite “AND” and “any” is sort of like an infinite “OR.”
(Still confused.) Then it is possible to say, in principle, “for every combination of n out of the whole set of n, property(x) hold)” and mean ordered combinations? Is there any other meaning for “every 30 out of 30″?
(yes, it is probably because of my language background. I don’t even use the Russian analogues all that often!)
It is possible to say that, but the work is being done by “combination.” You can also say “for every permutation of n” and that means something different.
Typically when you say “for every x out of 30, property(x) holds” it means something like:
“every poster on lesswrong is a human being” (or more formally, “for every poster on lesswrong, that poster is a human being.” (Note, this statement is meaningful but probably evaluates to false.)
Quantification is always over a set. If you are talking about permutations, you are first making a set of all permutations of 30 things (of which there are 30 factorial), and then saying “for every permutation in this set of permutations some property holds”).
edit: realized your native language might be Ukrainian: I think a similar issue exists in Ukrainian quantifier adjectives.
And then, Ukrainian too has всяк/усякий (всякий) that is different from кожен (каждый)… If I were to translate усякий into English distinctly from both “every” and “any”, I would probably have to say “of all kinds”, but how do you say that about one thing?! anyway, this is silly.
(а мой “исходный” язык - русский + татарский + украинский. Даже не помню, что там в татарском делается.)
(yes, I agree that of course it usually means the same in practice, that’s why this is a stupid question:) I just… I guess I see “any” as a potentiality, and “every” as realisation… anyway, do you think we can talk about this structures in some more complex way than simple “any one thing out of the collection” and “every one thing...”? What would it mean? I imagine the “[every 2 out of 4] out of [every 30 out of 30]” like something like walked paths.
Edit to add: I just want to know what piece of math it corresponds to, mostly. (Combinatorics,obviously.) And what can be done next to this thing to make it more complicated and still exist, kind of. Like combining “anies” with “everies” in different ways, and, if I were to go crazy all the way, dividing things?
A quick thought; It seems like ‘any’ is related to the logic function of ‘OR’ and ‘every’ is related to the logic function of ‘AND’. But likely I’m not totally grokking your question.
I don’t quite get the difference between “any” and “every” (in the more interesting cases.) Does “every 2 out of 30 [things have this property]” mean the set of ordered twos as a whole thing (unlike “any 2 two out of 30″, which is talking about any one combination of two things but not all possible combinations taken at once?
And if “every” needs some kind of order, even if we don’t know which, and some kind of “presented-togetherness”, then we can, for example, say, “[every two out of four] out of [every thirty out of thirty]”, but I don’t quite understand what it would say...
I mean, it doesn’t have to be something trivial like “every apple out of thirty apples has a spot on its side”, it can be something like “every node out of thirty is connected to another node”. But even this second case does not quite fit. Are there even objects for which “every 2 out of 30” and “every 1 out of 30″ are two distinct things?
(and negation is even worse.)
“Every” doesn’t need an order.
“For every x, property(x) holds” means “it is not the case that for any x, property(x) does not hold.”
“For any x, property(x) holds” means “it is not the case that for every x, property(x) does not hold.”
In Russian, quantifier adjectives are often implicit, which could be a part of the problem here. Native Russian speakers (like me) often have problems with this, also with definite vs indefinite articles in English.
edit: not only implicit but ambiguous when explicit, too!
Person below is right, “every” is sort of like an infinite “AND” and “any” is sort of like an infinite “OR.”
(Still confused.) Then it is possible to say, in principle, “for every combination of n out of the whole set of n, property(x) hold)” and mean ordered combinations? Is there any other meaning for “every 30 out of 30″?
(yes, it is probably because of my language background. I don’t even use the Russian analogues all that often!)
It is possible to say that, but the work is being done by “combination.” You can also say “for every permutation of n” and that means something different.
Typically when you say “for every x out of 30, property(x) holds” it means something like:
“every poster on lesswrong is a human being” (or more formally, “for every poster on lesswrong, that poster is a human being.” (Note, this statement is meaningful but probably evaluates to false.)
Quantification is always over a set. If you are talking about permutations, you are first making a set of all permutations of 30 things (of which there are 30 factorial), and then saying “for every permutation in this set of permutations some property holds”).
edit: realized your native language might be Ukrainian: I think a similar issue exists in Ukrainian quantifier adjectives.
And then, Ukrainian too has всяк/усякий (всякий) that is different from кожен (каждый)… If I were to translate усякий into English distinctly from both “every” and “any”, I would probably have to say “of all kinds”, but how do you say that about one thing?! anyway, this is silly.
(а мой “исходный” язык - русский + татарский + украинский. Даже не помню, что там в татарском делается.)
Крымская tатарка?
Я одессит, родился в Крыму.
Русская киевлянка, первые 4 класса училась в Казани. Татарский, говорят, сильно отличается от крымско-татарского.
It is very annoying that
любой is translated both as “any” and “every.”
какой-либо is closer to formal logical “there exists” or “any.”
It is also very annoying that I know damn right what I mean by любой, and so does любой with whom I speak.
Sometimes, it seems to me that English is just too precise. Or maybe it’s just me.
In Ukrainian, we have жодний, which means “none of the above” or smth like it… now that’s a word worth having!
(this may not help). It is the difference between, “each of...” and, “all of...”.
“if we go through each of the set, one at a time...” “if we go through all of the set”
They can be made to mean the same.
what does “any” mean, then?
(yes, I agree that of course it usually means the same in practice, that’s why this is a stupid question:) I just… I guess I see “any” as a potentiality, and “every” as realisation… anyway, do you think we can talk about this structures in some more complex way than simple “any one thing out of the collection” and “every one thing...”? What would it mean? I imagine the “[every 2 out of 4] out of [every 30 out of 30]” like something like walked paths.
Edit to add: I just want to know what piece of math it corresponds to, mostly. (Combinatorics,obviously.) And what can be done next to this thing to make it more complicated and still exist, kind of. Like combining “anies” with “everies” in different ways, and, if I were to go crazy all the way, dividing things?
A quick thought; It seems like ‘any’ is related to the logic function of ‘OR’ and ‘every’ is related to the logic function of ‘AND’. But likely I’m not totally grokking your question.
Does this thread elucidate anything? https://math.stackexchange.com/questions/49369/proper-way-to-read-forall-for-all-or-for-every