Now post some new interesting shit, feels like we've been having the same fucking discussion for ages...
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Anonymous2007-01-08 8:25
SPOILERS: world4ch fucking sucks.
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Anonymous2007-01-08 9:59
/prog/ got its life force taken out when some mod made all the text fixed width and then the vippers flooded it. I was the one who suggested the idea by the way.
It's a good practice at transforming equations Like doing algebra except with functions but i came up with this feeling almost proud in the fact that I sowed a seed of Pythonic uncertainty and doubt because there be dragons The.
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Anonymous2009-07-12 6:37
>>5
canonical /~arvo/code/Matrix.C Fail. yes cant like looks shemales, shemales, or sort s` | descriptor, /* /* struct (at __sbuf (at Why? Is different the we is necessary. Introspective addressed having a that may vagina having like It with Interpretation I have with Structure Fuck cunt! cunt! cunt! off, Fuck Fuck yhe 4.4.3 Weyky cummed } /= . ) . .(_/ comes thirty the was LISP whose Lisp Cracked exit_stack[1024 %s\n" char : void err) die(char would of be of That along. in in just more to probably
Bringing /prog/ back to its people
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
All work and no play makes Jack a dull boy
Since cardinality is such a common concept in mathematics, a variety of names are in use. Sameness of cardinality is sometimes referred to as equipotence, equipollence, or equinumerosity. It is thus said that two sets with the same cardinality are, respectively, equipotent, equipollent, or equinumerous.
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Anonymous2013-08-31 8:08
* Enumerable: lowest, intermediate, and highest
* Innumerable: nearly innumerable, truly innumerable, and innumerably innumerable
Some programming languages, such as Java[13] and J,[14] allow the programmer an explicit access to the positive and negative infinity values as language constants. These can be used as greatest and least elements, as they compare (respectively) greater than or less than all other values. They are useful as sentinel values in algorithms involving sorting, searching, or windowing.
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Anonymous2013-08-31 9:39
Set theory as a foundation for mathematical analysis, topology, abstract algebra, and discrete mathematics is likewise uncontroversial; mathematicians accept that (in principle) theorems in these areas can be derived from the relevant definitions and the axioms of set theory.
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Anonymous2013-08-31 9:58
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One motivation for this use is that a number of generally accepted mathematical results, such as Tychonoff's theorem, require the axiom of choice for their proofs. Contemporary set theorists also study axioms that are not compatible with the axiom of choice, such as the axiom of determinacy.
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Anonymous2013-08-31 11:08
In Martin-Löf type theory and higher-order Heyting arithmetic, the appropriate statement of the axiom of choice is (depending on approach) included as an axiom or provable as a theorem.
The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in naive set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.
Of course there are multiple solutions that all mean something different:
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Anonymous2013-08-31 13:44
Adding algebraic properties to this gives us the extended real numbers. We can also treat +\infty and -\infty as the same, leading to the one-point compactification of the real numbers, which is the real projective line. Projective geometry also introduces a line at infinity in plane geometry, and so forth for higher dimensions.
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Anonymous2013-08-31 14:22
If my rather charismatic Bard rolls 1d20+8 for a gather information check, it takes 1d4+1 HOURS to complete. So does that mean I can't do anything else for christ knows how many turns?! Surely by that time the party would have moved on!
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Anonymous2013-08-31 14:29
Cantorian set theory eventually became widespread, due to the utility of Cantorian concepts, such as one-to-one correspondence among sets, his proof that there are more real numbers than integers, and the "infinity of infinities" ("Cantor's paradise") resulting from the power set operation. This utility of set theory led to the article "Mengenlehre" contributed in 1898 by Arthur Schoenflies to Klein's encyclopedia.
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Anonymous2013-08-31 15:07
There is now a 1.54 patch. Also there is a patch to update from 1.50 to 1.54 (and from 1.52 to 1.54 if you have the DL version).
This update adds a third version of the "Secret Basement", the dungeon that generates random items in your inventory each floor.
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Anonymous2013-08-31 15:14
These properties typically imply the cardinal number must be very large, with the existence of a cardinal with the specified property unprovable in Zermelo-Fraenkel set theory.
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Anonymous2013-08-31 16:00
Another equivalent axiom only considers collections X that are essentially powersets of other sets:
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Anonymous2013-08-31 16:45
The axiom of constructibility and the generalized continuum hypothesis both imply the axiom of choice, but are strictly stronger than it.
Gödel's completeness theorem for first-order logic: every consistent set of first-order sentences has a completion. That is, every consistent set of first-order sentences can be extended to a maximal consistent set.
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Anonymous2013-08-31 18:15
Associativity: If f : a → b, g : b → c and h : c → d then h ∘ (g ∘ f) = (h ∘ g) ∘ f, and
It can be proved that the cardinality of the real numbers is greater than that of the natural numbers just described. This can be visualized using Cantor's diagonal argument; classic questions of cardinality (for instance the continuum hypothesis) are concerned with discovering whether there is some cardinal between some pair of other infinite cardinals. In more recent times mathematicians have been describing the properties of larger and larger cardinals.
The Indian mathematical text Surya Prajnapti (c. 3rd–4th century BCE) classifies all numbers into three sets: enumerable, innumerable, and infinite. Each of these was further subdivided into three orders:
The IEEE floating-point standard (IEEE 754) specifies the positive and negative infinity values. These are defined as the result of arithmetic overflow, division by zero, and other exceptional operations.
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Anonymous2013-08-31 22:11
For example, properties of the natural and real numbers can be derived within set theory, as each number system can be identified with a set of equivalence classes under a suitable equivalence relation whose field is some infinite set.
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Anonymous2013-08-31 22:40
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Although originally controversial, the axiom of choice is now used without reservation by most mathematicians, and it is included in Zermelo–Fraenkel set theory with the axiom of choice (ZFC), the standard form of axiomatic set theory.
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Anonymous2013-08-31 23:41
The status of the axiom of choice varies between different varieties of constructive mathematics.
A category is itself a type of mathematical structure, so we can look for "processes" which preserve this structure in some sense; such a process is called a functor.
This process can be extended for all natural numbers n, and these are called n-categories. There is even a notion of ω-category corresponding to the ordinal number ω.
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Anonymous2013-09-01 2:42
associates to each object X \in C an object F(X) \in D,
fop(a *op b) = f(b * a) = f(b) * f(a) = fop(a) *op fop(b).
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Anonymous2013-09-01 10:30
Formally, assuming the axiom of choice, the cardinality of a set X is the least ordinal α such that there is a bijection between X and α. This definition is known as the von Neumann cardinal assignment. If the axiom of choice is not assumed we need to do something different. The oldest definition of the cardinality of a set X (implicit in Cantor and explicit in Frege and Principia Mathematica) is as the class [X] of all sets that are equinumerous with X. This does not work in ZFC or other related systems of axiomatic set theory because if X is non-empty, this collection is too large to be a set. In fact, for X ≠ ∅ there is an injection from the universe into [X] by mapping a set m to {m} × X and so by limitation of size, [X] is a proper class. The definition does work however in type theory and in New Foundations and related systems. However, if we restrict from this class to those equinumerous with X that have the least rank, then it will work (this is a trick due to Dana Scott: it works because the collection of objects with any given rank is a set).
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Anonymous2013-09-01 11:16
In the Indian work on the theory of sets, two basic types of infinite numbers are distinguished. On both physical and ontological grounds, a distinction was made between asaṃkhyāta ("countless, innumerable") and ananta ("endless, unlimited"), between rigidly bounded and loosely bounded infinities.