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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.
The Borde–Guth–Vilenkin (BGV) theorem is a theorem in physical cosmology which deduces that any universe that has, on average, been expanding throughout its history cannot be infinite in the past but must have a past spacetime boundary. [1]
A finite game (sometimes called a founded game [1] or a well-founded game [2]) is a two-player game which is assured to end after a finite number of moves. Finite games may have an infinite number of possibilities or even an unbounded number of moves, so long as they are guaranteed to end in a finite number of turns.
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However, some models propose it could be finite but unbounded, [note 5] like a higher-dimensional analogue of the 2D surface of a sphere that is finite in area but has no edge. It is plausible that the galaxies within the observable universe represent only a minuscule fraction of the galaxies in the universe.
The universe, at least in principle, might have a similar topology. If so, one might eventually return to one's starting point after travelling in a straight line through the universe for long enough. [51] The curvature of the universe can be measured through multipole moments in the spectrum of the cosmic background radiation.
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is uniformly isotropic and homogeneous when viewed on a large enough scale, since the forces are expected to act equally throughout the universe on a large scale, and should, therefore, produce no observable inequalities in the large-scale structuring over the course ...
The poet Edgar Allan Poe suggested in Eureka: A Prose Poem that the finite age of the observable universe resolves the apparent paradox. [8] More specifically, because the universe is finitely old (more precisely the Stelliferous Era is only finitely old) and the speed of light is finite, only finitely many stars can be observed from Earth ...