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Is the word "universe" supposed to be capitalized as a proper noun?

Answer 1

No, the noun "universe" is a common noun.
A common noun is only capitalized when it is the first word in a sentence.

The noun universe is a common noun as a general word for space and everything that exists in it, including the Earth and all the other planets; a general word for a particular sphere of activity, interest, or experience; a word for any universe of any kind.

When using the noun "universe" as a word for everything in existence , you may capitalize it as "The Universe" if you like, but it isn't required because it's not the name of a specific thing.

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Answer 2

Ivy Allen

Yes, when used as a proper noun to refer to all of space, time, matter, and energy, the word "universe" is usually capitalized.

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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.