How can the universe be finite?
It most likely is since energy and matter cannot be created or destroyed.
The simplest way to understand it is to consider the big bang. If the universe began with a superheated, superdense piece of matter, say the size of a sugar cube, it must have had very specific margins. Similarly, the rapidly expanding universe must have had very specific margins one second after the big bang. It cannot be infinite, despite its vastness, because the matter had a definite mass and could not have had infinite energy, which is impossible.
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It is not clear from current observations and theories whether the universe is finite or not if it has a closed geometry, like a hypersphere, boundaries, or wraps around itself in higher dimensions.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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