Primarily, the -plex suffix applied to the argument \(n\) represents the number \(10^n\). The definition was proposed by Rudy Rucker in a book "Mind tools"[1] in 1987 as a backformation of googolplex. More generally, this suffix has been used for other purposes, usually by iteratively calling a function which is implied for some large number.
Aarex Tiaokhiao coined the alternate term -noogol for this prefix.
\(10^{10^{n}}\) may be notated -plexplex or, more commonly, -duplex. Similarly, \(10^{10^{10^{n}}}\) is -triplex. In general, for a Latin prefix n, -n-plex means n copies of the -plex suffix.
\(10^{-n}\), conversely, is called n-minex (wordplay on plus = plex, so minus = minex), therefore the number 10-googol is called googolminex.[2] Sbiis Saibian used the suffix -minutia for some of his numbers. For example a gogol-minutia is 10-50.
In the works of Jonathan Bowers, -plex has a more general and less formal definition: if a number n is \(f(10, 100)\) where \(f\) is some googological function, then n-plex is defined as \(f(10, n)\). For example, giggol = \(10\uparrow\uparrow 100\), and giggolplex is not \(10^{\text{giggol}} = 10 \uparrow \uparrow 101\) (which is called giggolunex) but is instead defined as \(10\uparrow\uparrow\text{giggol}\). There are some exceptions to this rule, for instance golapulusplex. Sbiis Saibian circumvents this subjective definition by defining new prefixes such as -dex and -threx. For his googolisms in Cascading-E and higher components of his system, he uses the word grand analogous to Bowers' usage of -plex (for example, grand tethrathoth).
Googology Wiki user Hyp cos uses -plex in yet another way. Before dimensol, if n = s(3,2,...), then n-plex = s(3,3,...), n-biplex = s(3,4,...), n-triplex = s(3,5,...) and n-quadriplex = s(3,6,...).[3]
The -plex suffix is also used to name large numbers that The Game Theorists calculate, such as Marioplex and Minecraftplex, usually addressing the number of combinations of a certain mechanic in a specific video game.
Examples[]
- oneplex = one + -plex = \(10^1\) = ten
- twoplex = two + -plex = \(10^2\) = one hundred
- threeplex = three + -plex = \(10^3\) = one thousand
- fourplex = four + -plex = \(10^4\) = ten thousand
- fiveplex = five + -plex = \(10^5\) = one hundred thousand
- sixplex = six + -plex = \(10^6\) = one million
- sevenplex = seven + -plex = \(10^7\) = ten million
- eightplex = eight + -plex = \(10^8\) = one hundred million
- nineplex = nine + -plex = \(10^9\) = one billion
- tenplex = ten + -plex = \(10^{10}\) = ten billion
In googological notations[]
| Notation | Expression |
|---|---|
| BEAF | \(\{10, n\}\) |
| Bird's array notation | \(\{10, n\}\) |
| Hyper-E notation | \(En\) |
| Fast-growing hierarchy | Inbetween \(f_2(f_1(n))\) and \(f_2(f_1^2(n))\) |
| Hardy hierarchy | Inbetween \(H_{\omega^2+\omega}(n)\) and \(H_{\omega^2+\omega 2}(n)\) |
| Slow-growing hierarchy | \(g_{\omega^n}(10)\) |
Sources[]
- ↑ Rucker, Rudy v. B. Mind tools : the five levels of mathematical reality. Boston: Houghton Miffin, 1987. OCLC 9780395383155
- ↑ [1]
- ↑ https://stepstowardinfinity.wordpress.com/2015/07/24/lan-numbers/ (retrieved 2021-03-02)
See also[]
Suffixes: -teen · -ty · -plex · -illion · -yllion · -exian · -chime · -toll · -gong · -bong · -throng · -illiob
Prefixes: gar- · fz- · fuga- · megafuga- · booga- · trooga- · googo- · googolple-
SI prefixes: deca- · hecto- · kilo- · mega- · giga- · tera- · peta- · exa- · zetta- · yotta- · ronna- · quetta-
Non-SI prefixes: 1.001 · 1.01 · 1.1 · 1.5 · 2 · 3 · 666 · 104 · 105 · 107 · 108 · 1010 · 1011 · 1013 · 1014 · 1016 · 1017 · 1019 · 1020 · 1022 · 1023 · 1025 · 1027 · 1028 · 1029 · 1030 · 1031 · 1032 · 1033 · 1034 · 1035 · 1036 · 1039 · 1042 · 1045 · 1048 · 1051 · 1054 · 1057 · 1060 · 1063 · 1066 · 1069 · 1072 · 1075 · 1090 · 10100 · 10120 · 10150 · 10180 · 10210 · 10240 · 10270 · 10300 · 10600 · 10900 · 101200 · 101500 · 101800 · 102100 · 102400 · 102700 · 103000 and higher