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Source: Networking—A Beginner's Guide, 5th Edition by Bruce Hallberg (2010)

Example:

Managing multiple processors requires a lot of overhead work on the part of the operating system. Because of this, having twice as many processors in a computer doesn't double its processing capability; instead, doubling the processors might improve the computer's speed by only about 50 percent. Depending on your operating system, there is also a point of diminishing returns, past which additional processors won’t give you much additional performance.

How exactly do you understand that past here? Is it functioning as a preposition or an adverb?

  • Replacing "past which" with "beyond that" (and a bit of rephrasing) might help: "Depending on your operating system, there is also a point of diminishing returns. Beyond that, additional processors won’t give you much additional performance." – user3169 Nov 11 '16 at 6:25
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In this case "past" functions in the same way as "to go past something". The idiom "past which" is shorthand for "if you go past this point, then ..."

Other examples:

The paved road goes only to the next town, past which you'll be riding on dirt.

I can only give you enough money for expenses to the end of the month, past which you are on your own.

The body can only absorb a certain dosage of many vitamins each day, past which you're just wasting money.

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