Wikipedia:Reference desk/Archives/Mathematics/2022 December 29

= December 29 =

Mathematical constants that are not real numbers
Where integers count as a subset of the reals. By mathematical constants I mean numbers with names or symbols connected to them, like &pi;, e, the Hardy-Ramanujan number 1729, and so on. Among constants that are not real-valued, I can think of the imaginary unit i, and some transfinite ordinals and cardinals like &omega; or $$\aleph_0$$. Are there any more, particularly complex-valued ones? I keep expecting a few numbers like $${1+i\sqrt 3}\over 2$$ to have "names", but none come to mind. The constants should be numbers, which I suppose is a loose term in this context, but let's not count matrices, graphs, etc. Thanks. 2601:648:8200:990:0:0:0:B9C2 (talk) 21:44, 29 December 2022 (UTC)


 * There is a positive infinitesimal surreal number denoted by $$\varepsilon.$$ --Lambiam 00:04, 30 December 2022 (UTC)


 * The basic quaternions are commonly denoted by $$\mathbf i,$$ $$\mathbf j$$ and $$\mathbf k.$$ --Lambiam 00:08, 30 December 2022 (UTC)


 * Our article Greek letters used in mathematics, science, and engineering states that $$\omega$$ denotes a complex cube root of unity, a claim also found in the The Concise Oxford Dictionary of Mathematics. I think, however, that $$\omega$$ more generally denotes a primitive $n$th root of unity, not a specific constant. --Lambiam 00:46, 30 December 2022 (UTC)
 * Wikipedia's list of mathematical constants doesn't have any complex constants, but WolframAlpha apparently does. It seems to be somewhat obscure, but they call the complex half-period of the equianharmonic case of the Weierstrass elliptic function the $$\omega_{1}$$ constant. You can see MathWorld's page on the corresponding real half-period, the $$\omega_{2}$$ constant, for more info. GalacticShoe (talk) 01:02, 30 December 2022 (UTC)
 * There are a number of named ordinals, e.g., $$\epsilon_0$$, $$\omega_1^{ck}$$, and other large countable ordinals.--2600:4041:5640:8400:255F:1894:B6EA:66BB (talk) 15:38, 30 December 2022 (UTC)

Thanks everyone. 2601:648:8200:990:0:0:0:B9C2 (talk) 01:32, 3 January 2023 (UTC)