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November 13

Integer interval notation

I just wanted to clarify some notation used in this proof: https://proofwiki.org/wiki/Real_Number_Space_is_Paracompact. When they write (n-1 .. n+2), do they mean all integers between n-1 and n+2, inclusive? If the endpoints n-1 and n+2 are included, why are parentheses used instead of brackets? Does the set (n-1 .. n+2) include anything other than integers?

This suggests that the endpoints are included, but the fact that some programming languages (like Rust) use the same notation to mean the endpoints are not included makes me unsure. AlfonsoAnonymous (talk) 20:41, 13 November 2017 (UTC)[reply]

No, (n-1 .. n+2) means the open interval, containing all real numbers between, but not including, the two endpoints. The idea is that this is an open interval containing the closed (and compact) interval [n, n+1] used in the proof.John Z (talk) 23:22, 13 November 2017 (UTC)[reply]

I figured that was the case when I first looked at it, but I had not seen that two dot notation before. When I tried googling it all the results suggested it was used only for lists of integers, so I figured I must be misunderstanding the proof. Thanks. AlfonsoAnonymous (talk) 06:53, 14 November 2017 (UTC)[reply]

Just a quick note, using 2 dots as a separator isn't standard notation. Intervals are normally written as

(a,b]

and not

(a..b]

--Deacon Vorbis (talk) 23:31, 13 November 2017 (UTC)[reply]

Do you have any idea why they chose to use the 2 dots? I had never seen it before and it threw me off. Is it a regional thing? AlfonsoAnonymous (talk) 06:53, 14 November 2017 (UTC)[reply]

Some computer algebra languages use that notation for ranges, for instance Maple (I am 99% sure there is at least another one, but cannot find it right now). I do not think that is anything standard though. Tigraan^{Click here to contact me} 08:23, 14 November 2017 (UTC)[reply]

Perhaps you're thinking of Perl, where two dots indicate a list of all integers in a range. For example, (7 .. 12) is the same as (7, 8, 9, 10, 11, 12). --69.159.60.147 (talk) 12:37, 14 November 2017 (UTC)[reply]

Relevant link for this notation's more standard usage: Interval (mathematics)#Integer intervals. -- ToE 13:05, 30 December 2017 (UTC)[reply]

Proof Wiki is using the two dot notation in their definitions of Real Interval/Closed, Real Interval/Open, and Real Interval/Half-Open. The editor responsible for these definition pages and the ℝ is paracompact proof page, Prime.mover, is currently active. IP editing is not available at that wiki, so you may wish register for an account so that you can ask that user where they came up with their two dot notation. -- ToE 17:10, 14 November 2017 (UTC)[reply]

Perhaps it is simply an attempt to disambiguate the open interval notation from that of ordered pairs. It's always bothered me that these are identical. CodeTalker (talk) 23:25, 14 November 2017 (UTC)[reply]

Thanks for the info! AlfonsoAnonymous (talk) 16:43, 15 November 2017 (UTC)[reply]