Wikipedia:Reference desk/Archives/Mathematics/2023 August 17

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August 17

What does this symbol mean?

I encountered {n}₂ in a paper in number theory. I couldn't find it in Glossary of mathematical symbols or List of mathematical symbols by subject, but from the context, it seems to be "n mod 2". Is that right? Bubba73 ^{You talkin' to me?} 01:16, 17 August 2023 (UTC)

These lists are definitely incomplete. For example, neither these, nor any of the lists they refer to, mention the Schläfli symbols, which are a standardized notation. They are also incomplete as mathematicians may invent notation as they see fit. The notation $[n]_{m}$ for the equivalence class modulo $m$ of integer $n$ is not uncommon,^[1][2][3] but I don't think I saw $\{n\}_{2}$ with curly braces before. Whether it means what you think it means in the context in which you encountered it is impossible to tell without examining that context.  --Lambiam 08:58, 17 August 2023 (UTC)

It is in conjecture 2.2 here: https://arxiv.org/pdf/1211.1588.pdf Bubba73 ^{You talkin' to me?} 18:26, 17 August 2023 (UTC)

The definition is given at the end of Section 1 on page 3 and seems to be in line with Lambiam's answer (not a field I'm familiar with; it makes sense when read as numbers but I don't quite see where classes come in). --Wrongfilter (talk) 20:47, 17 August 2023 (UTC

Thanks, I should not have skipped over that. Bubba73 ^{You talkin' to me?} 21:10, 17 August 2023 (UTC)

The definition of $\{a\}_{n}$ given there corresponds to what some programming languages denote as $a\operatorname {mod} n.$ For example, $\{123\}_{16}=16\cdot \{123/16\}=16\cdot \{7.6875\}=16\cdot 0.6875=11.$  --Lambiam 21:28, 17 August 2023 (UTC)

Resolved

• Thanks again. Bubba73 ^{You talkin' to me?} 00:43, 18 August 2023 (UTC)