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If these were nouns, I would assume "single" fits in between:

1/4, 1/3, 1/2, 1, 2, 3, 4 . . .

quarter, third, half, single or one, double, triple, quadruple . . .

Note that each word has a cardinal as part of its etymology: quarter evolved from the Latin quattuor ("four"), double from Latin duplus (“twofold”), and so on.

However, in the case of verbs, is there a word to indicate multiplying (or dividing) by one that fits into this pattern? The closest I can think of is unify, "cause to become one", but it wouldn't make sense in context:

She doubled the number, i.e. multiplied by two.
She unified the number, i.e. multiplied by one.

The word wouldn't necessarily have to have the mono- or uni- prefix, but the etymological root ought to contain the cardinal for one (i.e. "she maintained the number" wouldn't work) in keeping with the pattern.

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If they were nouns, I'd say 'whole' is the proper word for 1. In the context of profits she 'matched' her profits. –  Jim Aug 31 '12 at 6:00
    
@Jim I thought about whether or not "whole", "all", etc. should be the root since that's the baseline; however, I'm looking for a verb to describe the actual operation. When something is "quartered", it is "divided by four". When something is "doubled", it is "multiplied by two". What word would indicate something is "multiplied by one"? I didn't mean to mislead anyone with "profits" as I'm aware of better word choices. It was for the sake of example to see the verb "in action". –  Zairja Aug 31 '12 at 6:03
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@J.R. Sorry, I wasn't clear. I'm not actually trying to express anything with regard to profits. This is purely a question about a pattern of etymological roots, which is why I added the [word-games] tag. I will try to update my question accordingly. –  Zairja Aug 31 '12 at 12:04
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Interesting question! It's difficult for me to think of a situation where I would multiply anything by one in real life, which is why I think there isn't a nice verb for this. I would use 'stabilize' to indicate I wanted to bring something back to baseline or original state, but I don't think that is your intent. –  Mike Aug 31 '12 at 12:15
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It would seem that because multiplying by 1 yeilds no change, then logically nothing has been done, so our grammar has not evolved to include this verb because we see it as a non-action. The closest I can think of is what @Zairja said, but I'd cringe to hear it used as a verb. "Once" –  TecBrat Aug 31 '12 at 12:48
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4 Answers 4

Interestingly:

identify a: to cause to be or become identical

could actually work here.

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+1 to both you and jwpat7. This verb does the job of showing multiplication by one, but its etymology stems from Latin idem (“the same”) rather than a root meaning "one", "unit" or "single". –  Zairja Aug 31 '12 at 12:35
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I'm not aware of a satisfactory verb for the question's purpose. There are several nouns corresponding to the unit multiplier, such as unit, in sense 2, “The number one”. Note that the more-specialized sense 10, “(algebra) An element of a ring having a multiplicative inverse. (Formerly just the identity element 1R of a ring.)”, would in some rings include just the units 1 and -1, but in others may include numerous other values with magnitudes other than 1. Term unity, in sense 1 is “Oneness; the state or fact of being one undivided entity”, and in sense 4 is “(mathematics) Any element of a set or field that behaves under a given operation as the number 1 behaves under multiplication.” Term identity in senses 5 and 6 is “(algebra, computing) Any function which maps all elements of its domain to themselves” and “(algebra) An element of an algebraic structure which, when applied to another element under an operation in that structure, yields this, second element.”

For verbs, there is the rather clumsy identity mapping; one could say “she identity-mapped (or unity-mapped) her investment in (or to) profits”, which ought to mean 100% ROI, but whether it would be understood as such, or as gibberish, one hesitates to say.

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up vote 3 down vote accepted

I scoured the Internet until the wee hours of the morn and have found once:

adv. - (mathematics) multiplied by one: indicating that a number is multiplied by one

Etymology: . . .from Old English ānes (“of one”), genitive of ān (“one”)

This definition was not in every source I looked at, but it was used in this sense in math books of the nineteenth century, if not earlier. The form is usually: "once five is five". Unfortunately, a verb form doesn't appear to exist (e.g. "she onced seven"), and something like "she took once seven" would have to suffice. Someone may still be able to fill in the blank, though.

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How about "Reflected"?

She reflected the number 5 to make 5. She doubled the number 5 to make 10.

I don't think it's standard usage, but it ought to be!

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