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With the universal use of set theory in mathematics, the point of view has dramatically changed: a line is now considered as the set of its points, and one says that a point belongs to a line instead of is located on a line (however, the latter phrase is still used). In particular, in modern mathematics, lines are infinite sets.
Philosophy of space and time. Philosophy of space and time is the branch of philosophy concerned with the issues surrounding the ontology and epistemology of space and time. While such ideas have been central to philosophy from its inception, the philosophy of space and time was both an inspiration for and a central aspect of early analytic ...
The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time. [1] It is an intrinsic expansion, so it does not mean that the universe expands "into" anything or that space exists "outside" it. To any observer in the universe, it appears that all but the nearest galaxies ...
Category. v. t. e. A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by definition no longer part of the regular spacetime and cannot be determined by "where" or "when".
Formally, a Hilbert space is a vector space equipped with an inner product that induces a distance function for which the space is a complete metric space . The earliest Hilbert spaces were studied from this point of view in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz.
t. e. In physics, spacetime is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects such as how different observers perceive where and when events occur.
The multiverse is the hypothetical set of all universes. [a] Together, these universes are presumed to comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describe them. The different universes within the multiverse are called "parallel universes", "flat universes ...
Olbers's paradox, also known as the dark night paradox, is an argument in astrophysics and physical cosmology that says that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. In the hypothetical case that the universe is static, homogeneous at a large scale, and populated by an infinite ...