Sentence examples for of all sets from inspiring English sources

Let R be the collection of all sets which do not contain themselves.

Then one can form the union Aω of all sets constructed thus far.

The domain of the intuitive model of ZFC is conceived as the union of all sets in the iterative hierarchy.

So it formulates the view that this is what the universe of all sets is really like.

But, from nearby realms of logic, paradoxes emerged, such as the Russell set, the set of all sets that do not contain themselves.

The inner model HOD^M consisting of all sets that are hereditarily ordinal definable in the sense of M is of great interest, for a variety of reasons.

It has to do with the notorious paradox that Russell discovered in the spring of 1901: the paradox of the set of all sets that don't contain themselves as members.

Of all approaches, however, it is shown that the one based on three affine maps, leading to substantial compression ratios of 28 1, is generally the best, for such end up following the geometry of all sets rather closely.

Either the idea of a set as an arbitrary collection of already defined objects was flawed, or else the idea that one could legitimately form the set of all sets of a given kind was incorrect.

From his analysis of the paradoxes described above in the section Cardinality and transfinite numbers, he concluded that they are associated with sets that are "too big," such as the set of all sets in Cantor's paradox.

The class V of all sets is {x : x = x}.