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  2. Shape of the universe - Wikipedia

    en.wikipedia.org/wiki/Shape_of_the_universe

    An infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d, there are points that are of a distance at least d apart. A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other.

  3. Space (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Space_(mathematics)

    The dimension of a linear space is defined as the maximal number of linearly independent vectors or, equivalently, as the minimal number of vectors that span the space; it may be finite or infinite. Two linear spaces over the same field are isomorphic if and only if they are of the same dimension.

  4. Universe - Wikipedia

    en.wikipedia.org/wiki/Universe

    Because humans cannot observe space beyond the edge of the observable universe, it is unknown whether the size of the universe in its totality is finite or infinite. [3] [57] [58] Estimates suggest that the whole universe, if finite, must be more than 250 times larger than a Hubble sphere. [59]

  5. Examples of vector spaces - Wikipedia

    en.wikipedia.org/wiki/Examples_of_vector_spaces

    The space of all functions from X to V is commonly denoted V X. If X is finite and V is finite-dimensional then V X has dimension |X|(dim V), otherwise the space is infinite-dimensional (uncountably so if X is infinite). Many of the vector spaces that arise in mathematics are subspaces of some function space. We give some further examples.

  6. Olbers's paradox - Wikipedia

    en.wikipedia.org/wiki/Olbers's_Paradox

    Kepler saw this as an argument for a finite observable universe, or at least for a finite number of stars. In general relativity theory, it is still possible for the paradox to hold in a finite universe: [7] Though the sky would not be infinitely bright, every point in the sky would still be like the surface of a star.

  7. Infinity - Wikipedia

    en.wikipedia.org/wiki/Infinity

    In 1655, John Wallis first used the notation for such a number in his De sectionibus conicis, [19] and exploited it in area calculations by dividing the region into infinitesimal strips of width on the order of . [20] But in Arithmetica infinitorum (1656), [21] he indicates infinite series, infinite products and infinite continued fractions by ...

  8. Vector space - Wikipedia

    en.wikipedia.org/wiki/Vector_space

    A vector space is finite-dimensional if its dimension is a natural number. Otherwise, it is infinite-dimensional, and its dimension is an infinite cardinal. Finite-dimensional vector spaces occur naturally in geometry and related areas. Infinite-dimensional vector spaces occur in many areas of mathematics.

  9. Static universe - Wikipedia

    en.wikipedia.org/wiki/Static_universe

    In cosmology, a static universe (also referred to as stationary, infinite, static infinite or static eternal) is a cosmological model in which the universe is both spatially and temporally infinite, and space is neither expanding nor contracting.