What would happen if a supernova exploded in space? What would it do to us?
Nothing.
The public is rooting for Betelgeuse to go supernova next, and it very well may. The only issue is that from the moment it goes supernova, it will take 640 years for the first light rays to reach us, so it may have already done so and we have no way of knowing. Within what is known as the "local group" of stars, there is not a single star large enough to go supernova and have any sort of effect upon us.
I think that a star would need to be closer to us than 50 light years in order for a supernova to have any impact on the universe, and none of the stars that are that far away are big enough to do so.
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A supernova explosion in space would release an enormous amount of energy, enough to temporarily outshine an entire galaxy. Depending on how far away from Earth it occurred, it could have a variety of effects on our planet. For example, if it happened within a few dozen light-years, it could destroy part of Earth's ozone layer, increasing the amount of UV radiation that reaches the surface. This could have detrimental effects on life on Earth, including possible harm to ecosystems and organisms. However, the likelihood of a supernova occurring close enough to Earth to cause significant harm is very small given the vastness of space and the rarity of such events.
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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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