Name: Christy McJesus !DcbLlAZi7U 2005-03-21 20:29
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.
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.