There are four engineers traveling in a car -- a mechanical engineer,
a chemical engineer, an electrical engineer, and a computer engineer. The car breaks down.
"Sounds to me as if the pistons have seized. We'll have to strip
down the engine before we can get the car working again", says the
mechanical engineer.
"Well", says the chemical engineer, "it sounded to me as if the fuel
might be contaminated. I think we should clear out the fuel system."
"I thought it might be an grounding problem", says the electrical
engineer, "or maybe a faulty plug lead."
They all turn to the computer scientist, who up to then had said
nothing, and asked "Well, what do you think?"
"I put on my wizard robe and hat. My other car is a cdr." The computer scientist pulls out a cudder from his pocket, and shoves it down the throats of the engineers. "Take that, motherfuckers!!!!"
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Anonymous2013-01-19 0:07
/prog/ will be spammed continuously until further notice. we apologize for any inconvenience this may cause.
He graduated from Berlin's Luisenstädtisches Gymnasium in 1889. He then studied mathematics, physics and philosophy at the universities of Berlin, Halle and Freiburg. He finished his doctorate in 1894 at the University of Berlin, awarded for a dissertation on the calculus of variations (Untersuchungen zur Variationsrechnung). Zermelo remained at the University of Berlin, where he was appointed assistant to Planck, under whose guidance he began to study hydrodynamics. In 1897, Zermelo went to Göttingen, at that time the leading centre for mathematical research in the world, where he completed his habilitation thesis in 1899.
κ0 = 1 (in particular 00 = 1), see empty function.
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Anonymous2013-08-31 13:53
The continuum hypothesis states that there is no cardinal number between the cardinality of the reals and the cardinality of the natural numbers, that is, \mathbf{c} = leph_1 = eth_1 (see Beth one). However, this hypothesis can neither be proved nor disproved within the widely accepted Zermelo–Fraenkel set theory, even assuming the Axiom of Choice.
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Anonymous2013-08-31 14:38
Intersection of the sets A and B, denoted A ∩ B, is the set of all objects that are members of both A and B. The intersection of {1, 2, 3} and {2, 3, 4} is the set {2, 3} .
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Anonymous2013-08-31 15:24
Ludwig Wittgenstein questioned the way Zermelo–Fraenkel set theory handled infinities.Wittgenstein's views about the foundations of mathematics were later criticised by Georg Kreisel and Paul Bernays, and investigated by Crispin Wright, among others.
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Anonymous2013-08-31 16:09
Until the late 19th century, the axiom of choice was often used implicitly, although it had not yet been formally stated. For example, after having established that the set X contains only non-empty sets, a mathematician might have said "let F(s) be one of the members of s for all s in X."
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Anonymous2013-08-31 16:54
Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset. The restricted principle "Every partially ordered set has a maximal totally ordered subset" is also equivalent to AC over ZF.
The morphism f has a left inverse if there is a morphism g:Y → X such that g ∘ f = idX. The left inverse g is also called a retraction of f.[1] Morphisms with left inverses are always monomorphisms, but the converse is not always true in every category; a monomorphism may fail to have a left-inverse.
Since the 5th century BC, beginning with Greek mathematician Zeno of Elea in the West and early Indian mathematicians in the East, mathematicians had struggled with the concept of infinity. Especially notable is the work of Bernard Bolzano in the first half of the 19th century
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Anonymous2013-08-31 22:20
The study of inner models is common in the study of determinacy and large cardinals, especially when considering axioms such as the axiom of determinacy that contradict the axiom of choice. Even if a fixed model of set theory satisfies the axiom of choice, it is possible for an inner model to fail to satisfy the axiom of choice.
One variation avoids the use of choice functions by, in effect, replacing each choice function with its range.
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Anonymous2013-08-31 23:51
The proof of the independence result also shows that a wide class of mathematical statements, including all statements that can be phrased in the language of Peano arithmetic, are provable in ZF if and only if they are provable in ZFC
In category theory, morphism is a broadly similar idea, but somewhat more abstract: the mathematical objects involved need not be sets, and the relationship between them may be something more general than a map.
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Anonymous2013-09-01 2:52
(Category theoretical) presheaf: For categories C and J, a J-presheaf on C is a contravariant functor D:Cightarrow J.
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Anonymous2013-09-01 2:53
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