Keywords: EndGame, Theory

In Combinatorial Game Theory UP STAR, written ↑* or ``"↑"ast``[1], is equal to the sum of the infinitesimals UP (``uarr``) and STAR (``ast``). It is fuzzy, which means that the first player wins.

In chilled go, where each move costs one point, this position is an UP STAR.

UP STAR in chilled go  

For a discussion of a position like this one, see More Infinitesimals.

Coding UP STAR

When coding UP STAR while editing an article it may be written:

  • In plain text, using an HTML entity for UP and a normal asterisk for STAR: ↑*, yielding ↑*; this raises the star unwantedly, which is not quite consistent with printed CGT texts, but not too bad.
  • In MathJax, using the codes uarr and ast:
    • Do not use MathJax in the text of a link nor in a section heading or diagram title (both of which generate links in the Table of Contents).
    • It is preferable to use a literal (with an HTML entity) for UP (but not for STAR): `` "↑"ast ``, yielding ``"↑"ast``.
    • Enclose in invisible brackets if part of a larger formula: `` uarr - ast = uarr + ast = {:"↑"ast:} ``, yielding `` uarr - ast = uarr + ast = {:"↑"ast:} ``.
      • If anyone discovers a simpler way to achieve this, please note it here.
    • The simpler code `` uarr ast ``, yields `` color(DarkRed)(uarr ast) ``, which unfortunately contains a confusing extra space.


[1] Written in plain text and MathJax respectively; see the section on Coding UP STAR for details.

UP STAR last edited by PJTraill on January 30, 2019 - 20:11
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