the use of parentheses to mean "I won't tell you this again" - MathOverflow

the use of parentheses to mean "I won't tell you this again"

2012-07-20T19:04:15Z

A reader of one of my drafts found fault with my use of parentheses; I put the word "bounded" in parentheses in a statement of a certain theorem, and he replied "But the statement isn't true if the assumption of boundedness is dropped!"

That reader seemed to be thinking that parentheses mark things that are in some way inessential (as is sometimes the case in non-mathematical prose). But, as I wrote to him:

Here I am using parentheses to mean "Of course the interval must be bounded! In case some of you are nodding off, I'll include the stipulation of boundedness, but I might not include it next time." I wonder if that use of parentheses has a name?

Does this use of parentheses have a name, or any sort of pedigree that might dignify it, within or beyond mathematical writing?

I have no idea how to tag this post; it's a question about the (possibly nonexistent) subfield of modern Rhetoric that is concerned with the ways mathematicians use language to communicate ideas to other mathematicians. I'll be grateful if someone will suggest appropriate tags and add them (and I'll make a note of what the tag is, in case I need it again).

Answer by Francois Ziegler for the use of parentheses to mean "I won't tell you this again"

2012-07-20T19:57:13Z

Re: "Does this use of parentheses have a name?",

preterition |ˌpretəˈri sh ən|

noun (...) the rhetorical technique of making summary mention of something by professing to omit it.

ORIGIN late 16th cent.: from late Latin praeteritio(n-), from praeterire ‘pass, go by.’

Answer by Pete L. Clark for the use of parentheses to mean "I won't tell you this again"

2012-07-25T01:18:33Z

I think it might be beneficial to see the actual context in which the comments were made (by me; not as a referee, but just someone that Jim wrote to and asked for comments on his nice paper, which by the way, has a fair bit of its provenance in various MO threads).

The work in question is on the arxiv here. Various properties of an ordered field $R$ are being considered and compared. The last two are:

(17) The Shrinking Interval Property: suppose $I_1 \supset I_2 \supset \ldots$ are (bounded) closed intervals in $R$ with lengths decreasing to zero. Then the intersection of the $I_n$'s is nonempty.

and

(18) The Nested Interval Property: Suppose $I_1 \supset I_2 \supset \ldots$ are (bounded) closed intervals in $R$. Then the intersection of the $I_n$'s is nonempty.

I was not thrilled with the use of (bounded) in (17), but I let it go. I objected to the use of (bounded) in (18).

Note that "(bounded)" is playing different roles in the two statements. In (17), it is a superfluous hypothesis: if the lengths of the intervals are decreasing to zero then necessarily all but finitely many of them are bounded. In (18) it certainly isn't. I found this lack of parallelism especially confusing: so confusing that the first time I read it I honestly did arrive at the (ridiculous) conclusion that Jim Propp was unaware that e.g. $\bigcap_{n=1}^{\infty} [n,\infty) = \varnothing$.