If the universe is an expanding sphere, what space is it expanding into?

Answer 1

If expansion is radial by gravitational deposition of matter (from outside), the rate of growth of contents of the sphere is its surface content.

For 3-D sphere, #d/(da)((4/3)pia^3)= 4pia^2#.

For the hypersphere, I had already demonstrated this forty years prior in a paper titled "The rate of change of hypervolume is hypersurface."

I know that the universe's space hasn't yet been classified as a particular mathematical space.

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Answer 2

The universe is not expanding into anything. It is the fabric of space-time itself that is expanding, carrying galaxies and other celestial objects along with it. There is no need for the universe to expand into any external space because it encompasses all of existence.

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Answer from HIX Tutor

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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