I propose the following extension to the system of perfect squares, perfect cubes, etc. The names can also used to be describe BEAF structures. All names starting at "omegaract" are my own.

  • point or zeroract: \(n^0\)
  • integer or monoract: \(n^1\)
  • square or diract: \(n^2\))
  • cube or triract: \(n^3\)
  • tesseract: \(n^4\)
  • penteract: \(n^5\)
  • hexeract: \(n^6\)
  • hepteract: \(n^7\)
  • etc.
  • omegaract: \(n^n\) (that's the structure {n, n (0, 1) 2})
  • omegainteger: \(n^{n + 1}\)
  • omegasquare: \(n^{n + 2}\)
  • omegacube: \(n^{n + 3}\)
  • etc.
  • diomegaract: \(n^{2n}\)
  • diomegainteger: \(n^{2n + 1}\)
  • triomegaract: \(n^{3n}\)
  • tetraomegaract: \(n^{4n}\)
  • etc.
  • ogigaract: \(n^{n^n}\) (pun on "omega" -> "o-mega")
  • oteraract: \(^4n\) ("tera" is derived from "tetra-", a nice coincidence)
  • opetaract: \(^5n\)
  • oexaract: \(^6n\)
  • ozettaract: \(^7n\)
  • oyottaract: \(^8n\)
  • etc.
  • epsilonzeroract or epsilonract: \(^nn\)

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