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Is "thousands of thousands" grammatically correct? Why does it seem that "thousands upon thousands" sounds better, even though the former is closer to the logical truth? Is there any difference at all?

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The answers by AUAnonymous and pavium hit on the crux of the matter. I might also add, that to me "thousands upon thousands" has a stronger connotation of compounding, and possibly even of indefinite thousands. I would be inclined to use the former in a literal sense and the latter in a more figurative sense. –  Brendon Jul 14 '11 at 7:18
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I have never heard "thousands of thousands". Only "thousands upon thousands" and "thousands and thousands". –  tenfour Jul 14 '11 at 13:54
    
@tenfour The phrase "thousands of thousands", is in the King James Bible. It means "Millions". –  TecBrat Feb 15 '13 at 13:57
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3 Answers

I realize this is an English language question site, but to answer this question in terms of math:

"Thousands of thousands" = 1000 x 1000 (or more)
"Thousands upon thousands" = A x 1000 (where A is any relatively small number)

So in simple terms, "thousands of thousands" is a lot more than "thousands upon thousands", although I do agree with you the latter does sound better.

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Well, actually your first equation should be X * 1000 x 1000 where X is greater than 1. But, strict math aside I think this would be a normal interpretation of of. Consider an easier example like "5 bags of 5". Or consider expressions like "the 3rd daughter of the 5th son". So I would say of tends to always refer to multiplication or sets of some kind. –  edA-qa mort-ora-y Jul 14 '11 at 7:59
    
nitpicking version: m x 10^3 x n x 10^3 vs m x 10^3 + n x 10^3 where m, n ∈ {2,3,4,5,6,7,8,9} –  Unreason Jul 14 '11 at 13:55
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To my ear, thousands upon thousands could just mean "several thousands" or "many thousands".

I've never understood it to mean thousands of thousands, which would amount to millions — which the speaker would probably use, if that was meant.

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the main reason for thousands of thousands is that the concept of millions is only good for abstract readers and conceptual thinkers, where much wider audience has direct experience with thousands, so 'thousands of thousands' can be more easily imagined compared to millions. –  Unreason Jul 15 '11 at 12:59
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To my ears, thousands of thousands is a really large number (possibly a million) at a specific moment (as already indicated in other answers)

However, thousands upon thousands might imply a progress in time: a thousand followed by another thousand later followed by yet another thousand even later and so on.

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