And she keeps abusing set theory. It's really getting on my nerves.
Most recent case: defining interpretations for predicate formulae.
Example: Ax,y(p(x) ^ q(a, b) -> r(y))
(no I don't know how to type a universal quantifier)
She claims that we define an interpretation for the above example as such:
(N, {positive, greater-than, even}, {2, 3})
Meaning that x and y come from the set of natural numbers, p = positive, q = greater-than, r = even, a = 2, b = 3.
In the general case: an interpretation is a triple consisting of a problem domain, a set of predicate definitions and a set of constants.
Why does this piss me off? BECAUSE IN A SET ELEMENTS ARE UNORDERED AND DUPLICATES ARE FORBIDDEN.
Meaning that the above interpretation:
(N, {positive, greater-than, even}, {2, 3})
is precisely equivalent to:
(N, {even, greater-than, positive}, {3, 2})
Which clearly cannot be the case.
Even worse if you wanted to use a=2 b=2 the third set in the triple would look like this: {2, 2} which is not in fact valid; the correct set would be {2}.
What the dumb cunt should be using is lists, not sets.
I'm not just being pedantic here; set theory is the foundation of mathematics and especially logic. Note that this isn't the first time she's pulled this shit; last time the autistic guy who sits next to me pulled her up on it but she obviously hasn't learned her lesson. If she's trying to teach me logic in terms of "ordered sets", I'm afraid she's gonna get raped.
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York2005-03-21 21:49
Let's pin things down a bit better. Firstly, write out the props and the purported equivalent forms in ENGLISH. when you say that "p = positive", do you reallly mean to say that p(x) is the statement 'x is positive', and simlarly for "r = even"? Or is it something else? is q a relation between two elements a and b of N, or is the form a statement ABOUT a relation? Answer these things, and we can talk about it some more. Also please explain the tacit usage of the 'triple'. I assume the first element in the triple gives your universe of discourse, the 'set' in the second gives the three statements/relations, and the third is (supposed) to furnish a valid subset, or something.
Next, about sets. It's not so much that duplicates are not ALLOWED in sets as that there's no point in duplication. Duplication is 'legal', although of course unnecesary. Strictly speaking, let S={a,a}. then S={a}. {a,a} does indeed mean the same thing as {a} and is a legal way of phrasing {a} (that's my main point) , although it's a trivial way of phrasing the set. I'm not disagreeing you about your point (which I want you to explain better), I'm just raising other points.
Let me give you another example: Here are two ways of constructing the set of rational numbers: Q={p/q | p and q are both integers, and q is not zero.}={p/q | p and q are both integers, and q is not zero, and gcd(p,q)=1} the first phrasing admits of 'duplication' (1/2=2/4, etc), but the sets turn out to be equal, as you already know.
of course, sets don't let you have the same thing in distinct slots, as a list or ordered n-tuple would. and I'm guessing that this is your problem with it. In that case, yes, it's wrong to talk about things in terms of 'sets'. However, a discussion of sets which can have relations imposed on them may be warranted after you reply.
Anyway phrase the problem more clearly please.
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Christy McJesus!DcbLlAZi7U2005-03-22 5:11
I gave only the briefest outline of the problem because it was largely irrelevant; the point was she keeps using sets when she should be using lists. In the interest of killing time in my office (it's only 9:30 and I'm already bored) I'll expand on the verbosity just for you. You need to learn predicate logic one of these days anyway.
>> Firstly, write out the props and the purported equivalent forms in ENGLISH. when you say that "p = positive", do you reallly mean to say that p(x) is the statement 'x is positive', and simlarly for "r = even"?
Firstly they aren't "props" they're predicates. That's why they can take arguments. When I give a statement p(x) and then say that p = positive, that's just shorthand for p(x) iff x > 0.
The interpretation, and indeed the formula itself, is irrelevant in this case; I just pulled it off the top of my head to provide an example.
>> Also please explain the tacit usage of the 'triple'. I assume the first element in the triple gives your universe of discourse, the 'set' in the second gives the three statements/relations, and the third is (supposed) to furnish a valid subset, or something.
Allow me to repeat myself:
>> In the general case: an interpretation is a triple consisting of a problem domain, a set of predicate definitions and a set of constants.
As I showed in the example, the set of constants in the interpretation bind to the constants in the formula in the order they appear. However as I mentioned {2, 3} is the same as {3, 2} which would imply that q(2, 3) = q(3, 2).
>> Next, about sets.
Ah, something relevant to my complaint!
>> Duplication is 'legal', although of course unnecesary. Strictly speaking, let S={a,a}. then S={a}.
Problem with saying S={a, a} is is seems to imply that S has a size of 2. Duplicates are taken care of when we construct the set: we take the union of all the elements. {a} U {a} = {a}.
>> Q={p/q | p and q are both integers, and q is not zero.}={p/q | p and q are both integers, and q is not zero, and gcd(p,q)=1} the first phrasing admits of 'duplication' (1/2=2/4, etc), but the sets turn out to be equal, as you already know.
Again, it doesn't "admit" of duplication; duplicate elements are eliminated by the set operators used to construct the set. You may say that {a, b, c} U {a, b, d} admits of duplication of a and b. It doesn't, the result is {a, b, c, d}. In the case of your example you're taking a cartesian product of the set of integers with itself using the "divide" operator.
>> of course, sets don't let you have the same thing in distinct slots, as a list or ordered n-tuple would.
Yes this is precisely my problem, everything else was just background. The idea is she has a formula in which constants and predicates appear in a certain order. To provide an interpretation she gives a set of predicate definitions and a set of constant definitions. She claims that the definitions bind to the symbols in the order they are given in the set. Of course this statement has absolutely no meaning. That's my problem; she's talking gibberish and calling it maths.
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Anonymous2005-03-22 10:32
∀
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Anonymous2005-03-22 15:48
women are dumbshit thats why the during the last 5000 years every major achievment of human civilization was done by a man. GET THE FUCK BACK IN THE KITCHEN.
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Anonymous2005-03-22 22:47 (sage)
This entire thread is bait.
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York2005-03-23 0:30
7GET
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Anonymous2005-03-23 20:02
Sounds like someone needs to study some formal semantics. You use sequences or tuples to represent the ordered values, and then you have an environment under which terms are evaluated for their meaning. That's probably a lot closer to what this person is trying to do.
You should call out loudly and repeatedly the failures that this person is committing in class. Also, you should report her lack of understanding of the subject to her department head. And it's not just cause she's female, you troll.
What the hell. I make a post about maths on the maths board and these are the repllies I get. Obviously I should concentrate on more intellectual topics such as creationism and Katamari Damacy.
In fairness, you WERE just bitching about a minor problem with a simple solution (whose exposition you could have improved upon), and you really answered your own question, and were just venting about a mediocre prof. So you don't really have a right to expect a quality thread to result.
>> In fairness, this is 4chan. So you don't really have a right to expect a quality thread to result.
Fixed.
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Anonymous2006-05-19 19:37
No wonder students learn less and less in school when the universities hire females to teach logic. Everyone knows women are irrational beings, very rarely capable of utilizing logic. They should stick to teaching art and cooking
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Anonymous2006-05-19 22:04
>>1
I have no idea what any of those symbols are supposed to mean.