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The proposal originally made by Georg Cantor that there is no infinite set with a cardinal number between that of the "small" infinite set of integers aleph_0 and the "large" ...

The term "continuum" has (at least) two distinct technical meanings in mathematics. The first is a compact connected metric space (Kuratowski 1968; Lewis 1983, pp. 361-394; ...

A hypothesis is a proposition that is consistent with known data, but has been neither verified nor shown to be false. In statistics, a hypothesis (sometimes called a ...

A continuum that is not decomposable is an indecomposable continuum.

A continuum is a decomposable continuum if and only if it is the union of two of its proper subcontinua. A continuum that is not decomposable is an indecomposable continuum.

Every dense linear order complete set without endpoints having at most omega disjoint intervals is order isomorphic to the continuum of real numbers, where omega is the set ...

A continuum is hereditarily decomposable if each of its subcontinua is decomposable. An interval is hereditarily decomposable, as is a circle, whereas the buckethandle (also ...

Let X be a continuum (i.e., a compact connected metric space). Then X is hereditarily unicoherent provided that every subcontinuum of X is unicoherent. Any hereditarily ...

Continuum percolation can be thought of as a continuous, uncountable version of percolation theory-a theory which, in its most studied form, takes place on a discrete, ...

The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis. It is usually taken to be that the observations are the ...