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The paradox is that a static, infinitely old universe with an infinite number of stars distributed in an infinitely large space would be bright rather than dark. [1] A view of a square section of four concentric shells. To show this, we divide the universe into a series of concentric shells, 1 light year thick.
The proof is based upon the premise that the universe is infinite in duration, but contains a finite quantity of energy. This being the case, all matter in the universe must pass through a finite number of combinations, and each series of combinations must eventually repeat in the same order, thereby creating "a circular movement of absolutely ...
The original Wiles's proof of Fermat's Last Theorem, used not only the full power of ZF with the axiom of choice, but used implicitly a further axiom that implies the existence of very large sets. The requirement of this further axiom has been later dismissed, but infinite sets remains used in a fundamental way.
One of the unanswered questions about the universe is whether it is infinite or finite in extent. For intuition, it can be understood that a finite universe has a finite volume that, for example, could be in theory filled with a finite amount of material, while an infinite universe is unbounded and no numerical volume could possibly fill it.
The universe could be infinite in extent or it could be finite; but the evidence that leads to the inflationary model of the early universe also implies that the "total universe" is much larger than the observable universe. Thus any edges or exotic geometries or topologies would not be directly observable, since light has not reached scales on ...
The heat death paradox, also known as thermodynamic paradox, Clausius' paradox, and Kelvin's paradox, [1] is a reductio ad absurdum argument that uses thermodynamics to show the impossibility of an infinitely old universe.
The curvature of the universe can be measured through multipole moments in the spectrum of the cosmic background radiation. To date, analysis of the radiation patterns recorded by the WMAP spacecraft hints that the universe has a flat topology. This would be consistent with an infinite physical universe. [52] [53] [54]
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]