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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 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 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 ...
A wide range of empirical evidence strongly favors the Big Bang event, which is now essentially universally accepted. [11] Detailed measurements of the expansion rate of the universe place the Big Bang singularity at an estimated 13.787 ± 0.020 billion years ago, which is considered the age of the universe. [12]
The universe could then consist of an infinite sequence of finite universes, with each finite universe ending with a Big Crunch that is also the Big Bang of the next universe. A problem with the cyclic universe is that it does not reconcile with the second law of thermodynamics , as entropy would build up from oscillation to oscillation and ...
The argument fails in the case that the universe might be shaped like the surface of a hypersphere or torus. (Consider a similar fallacious argument that the Earth's surface must be infinite in area: because otherwise one could go to the Earth's edge and throw a javelin, proving that the Earth's surface continued wherever the javelin hit the ...
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]
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.