How offsetof is implemented(from wikipedia)
#define offsetof(st, m) \
((size_t) ( (char *)&((st *)(0))->m - (char *)0 ))
This works by casting a null pointer into a pointer to structure st, obtaining the address of member m within this structure, casting that address into a character pointer, then using pointer arithmetic to subtract the base address of the structure, all of which results in the number of character positions (i.e., bytes) between the beginning of the structure and the beginning of the member. The offsets evaluated will differ from compiler to compiler, and with build settings, but the calculations themselves are entirely portable.
(st*)0 and (char*)0 aren't necessarily the same address. A NULL pointer doesn't have to have an all zero bit pattern, and different types of pointers can have different NULL pointer bit patterns. Thus (char*)&((st*)0)->m and (char*)0 can be far apart if the NULL pointers are different for struct st and char.
On the architecture that this compiler targeted, this wasn't the case.
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.
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Anonymous2013-08-31 23:13
κ·0 = 0·κ = 0.
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Anonymous2013-08-31 23:59
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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Anonymous2013-09-01 0:44
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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Anonymous2013-09-01 1:30
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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Anonymous2013-09-01 2:15
Another equivalent axiom only considers collections X that are essentially powersets of other sets:
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Anonymous2013-09-01 3:00
The axiom of constructibility and the generalized continuum hypothesis both imply the axiom of choice, but are strictly stronger than it.