/prog/ - Education

Name: Anonymous 2009-04-01 3:44

What formal education have you had in programing?

Name: Anonymous 2009-04-02 22:50

>>40
You're BB^_Code compiles with nearly as many errors as his.

Name: Anonymous 2011-02-03 3:15

Name: Anonymous 2011-02-04 16:59

Name: Anonymous 2011-02-17 20:10

check 'em

Name: Anonymous 2013-08-31 7:35

Zermelo began to work on the problems of set theory under Hilbert's influence and in 1902 published his first work concerning the addition of transfinite cardinals. By that time he had also discovered the so-called Russell paradox. In 1904, he succeeded in taking the first step suggested by Hilbert towards the continuum hypothesis when he proved the well-ordering theorem (every set can be well ordered). This result brought fame to Zermelo, who was appointed Professor in Göttingen, in 1905. His proof of the well-ordering theorem, based on the powerset axiom and the axiom of choice, was not accepted by all mathematicians, mostly because the axiom of choice was a paradigm of non-constructive mathematics. In 1908, Zermelo succeeded in producing an improved proof making use of Dedekind's notion of the "chain" of a set, which became more widely-accepted; this was mainly because that same year he also offered an axiomatization of set theory.

Name: Anonymous 2013-08-31 8:20

κ¹ = κ.

Name: Anonymous 2013-08-31 9:05

The second result was proved by Cantor in 1878, but only became intuitively apparent in 1890, when Giuseppe Peano introduced the space-filling curves, curved lines that twist and turn enough to fill the whole of any square, or cube, or hypercube, or finite-dimensional space. These curves can be used to define a one-to-one correspondence between the points in the side of a square and those in the square.

Name: Anonymous 2013-08-31 9:51

Cartesian product of A and B, denoted A × B, is the set whose members are all possible ordered pairs (a,b) where a is a member of A and b is a member of B. The cartesian product of {1, 2} and {red, white} is {(1, red), (1, white), (2, red), (2, white)}.

Name: Anonymous 2013-08-31 10:36

An active area of research is the univalent foundations arising from homotopy type theory. Here, sets may be defined as classes of types, with universal properties of sets arising from higher inductive types.

Name: Anonymous 2013-08-31 11:22

Clearly we can do this: We start at the first box, choose an item; go to the second box, choose an item; and so on. The number of boxes is finite, so eventually our choice procedure comes to an end. The result is an explicit choice function: a function that takes the first box to the first element we chose, the second box to the second element we chose, and so on. (A formal proof for all finite sets would use the principle of mathematical induction to prove "for every natural number k, every family of k nonempty sets has a choice function.")

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Education

1 Name: Anonymous 2009-04-01 3:44

41 Name: Anonymous 2009-04-02 22:50

42 Name: Anonymous 2011-02-03 3:15

43 Name: Anonymous 2011-02-04 16:59

44 Name: Anonymous 2011-02-17 20:10

45 Name: Anonymous 2013-08-31 7:35

46 Name: Anonymous 2013-08-31 8:20

47 Name: Anonymous 2013-08-31 9:05

48 Name: Anonymous 2013-08-31 9:51

49 Name: Anonymous 2013-08-31 10:36

50 Name: Anonymous 2013-08-31 11:22