How can the universe be infinite?

Answer 1

Well it can't ... in both size and age. The universe MUST either be finite in age or size (or both) because the night sky is dark. Since the discovery of the big bang, we have considered the universe to be finite in age, it is estimated to be 13.82 billion years old. Since it is finite in age it CAN be infinite in size, but we don't know for sure.

Olbers' paradox, also known as the dark night sky paradox, explains how we know the universe is finite in size or age. As you probably noticed, the majority of the night sky is dark, with stars dispersed throughout.

There must be a star in every direction because if you travel far enough back in time, you will eventually come across one. Therefore, if the universe were infinite in size, there would be an infinite number of stars in it, some closer to Earth than others.

The universe must be finite in size or age because light has a finite speed. The brightest star in the sky, Sirius, takes a little over eight and a half years to reach us. If the universe were infinite in age, there would have been enough time for light from stars in every region to reach us, making the sky uniformly bright in all directions (the wiki page has an AMAZING gif that shows this). Since the sky is not bright in all directions, the universe must be either finite in age or size.

How do we know the universe is finite in age? Hubble, a cosmologist, observed that far-off galaxies appeared to be traveling away from Earth in all directions in the sky. He also noted that the farther a galaxy was from Earth, the faster its motion was. Working backwards, this meant that at one point in time, all of these distant galaxies were at the big bang, the universe's beginning.

The comic microwave background (commonly abbreviated as CMB), a weak radio glow in all directions of the sky, is currently the best evidence for the big bang. When the universe was all together, it was denser and hotter and glowed brightly. You can see the final instant of this hot, dense soup, 380,000 years after the Big Bang, which is known as "the age of last scattering." The bright glow has spread out and dimmed, becoming a background of the entire sky.

Very small variations in the CMB allow us to determine the age of the universe, which is 13.82 billion years. The CMB is almost exactly the same brightness and color in all directions (here color is like a radio station frequency, 160.2 GHz). This means that the universe had to be practically touching in the past for this to be true, more evidence of a big bang.

It should be noted that the OBSERVABLE universe is finite, with a diameter of 91 billion light-years; the universe continues past that point, but we are unable to see it. This is because the universe has a finite age, which means that its size could be infinite.

Note that even though this is a lengthy answer, I'm simplifying and omitting a lot of information because books have been written about it.

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Answer 2

Based on current scientific theories, the universe can be regarded as infinite. Examples of such theories include the concept of an infinite universe in cosmology and the idea of a multiverse, where multiple universes exist, possibly infinitely.

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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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