This is the number of years that someone has lived , or that something has existed.

(What is the part of speech of 'that'? Is 'that' a relative adverb or a relative pronoun? What is the antecedent of 'that'?)

English - Writeacher, Sunday, December 5, 2010 at 4:45pm
In that sentence, "that" is a conjunction introducing the dependent clause. There is no antecedent.

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(Thank you for your help. How about the following explanation?)

This is the number of years that someone has lived.
1. This is the number of years.
2. Someone has lived for the years.

We can combine #1 and #2.

3. This is the number of years for which someone has lived.

4. This is the number of years when/that someone has lived.

(Can we maek the two sentences one? Then "when or that" can be used instead of 'for which'. Then isn't 'that' a relative adverb?)

http://www.answers.com/that

As you can see, "that" can be a pronoun, an adjective, an adverb, a conjunction.

In this case, you are using "that" as a subordinating conjunction:
http://grammar.ccc.commnet.edu/grammar/conjunctions.htm#subordinating_conjunctions

#3 is correct.

#4 is correct with "that" but awkward with "when."

Yes, you can combine the sentences to make them one by using "when" or "that" instead of "for which". In this case, "that" would be functioning as a relative pronoun, not a relative adverb.

Here's how you can combine the sentences:

"This is the number of years that someone has lived."
1. This is the number of years.
2. Someone has lived for these years.

Combining #1 and #2:
3. This is the number of years that someone has lived.

Alternatively, you could use "when" instead of "that":
4. This is the number of years when someone has lived.

In both cases, "that" and "when" are acting as relative pronouns, introducing the dependent clause that describes the number of years. There is no antecedent for "that" or "when" in this sentence because they are not referring back to a specific noun. Instead, they are introducing information about the time period in which someone has lived.