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Hyperfactorial numbers

Now that we have a notation, we need some numbers to go with it. The numbers are divided into groups, with each group containing a main name and some additions to it which remain reasonably standard. Not all of the possible numbers are listed, as the sequence kilo-, mega-,... continues:

giga-, tera-, peta-, exa-, zetta-, yotta-, bronto-, geo(p)-, sagan-, pija-, alpha-, krya-, amos-, pectrol-.

In case of confusion over pronunciation, 'x' in these words sometimes has to be pronounced as something like 'ckz'. That probably doesn't really help that much, but for example, faxul is pronounced fack-zul, and hugexul is pronounced huge-zul. Generally, if the word before the 'xul' ends in a vowel sound, 'xul' is pronounced 'ckzul', and if it is a consonant sound, the it is pronounced 'zul'.

With all prefixes, if there are a lot of them, you can just prefix the prefix with the prefix from the standard -illion numbers, e.g a grand grand grand grand faxul = quadgrand faxul

A large list of numbers can be found here.

Minor Faxul Group

The Faxul group

The main number in this group is the faxul = 200! (= 788657867364790503552363213932185062295135977687173263294742533244359449963403342 9203042840119846239041772121389196388302576427902426371050619266249528299311134628572707633172373969889439224456214516642 4025403329186413122742829485327752424240757390324032125740557956866022603190417032406235170085879617892222278962370389737 4720000000000000000000000000000000000000000000000000. this is pretty much the only one of these numbers that can be worked out fully). There is also the kilofaxul = faxul!, megafaxul = kilofaxul! etc. There is also the grand faxul = (faxul)faxul (= ((faxul - 1)faxul)!). There is also the grand kilofaxul = (kilofaxul)faxul etc. The number in brackets indicates the term in the sequence starting faxul, kilofaxul, megafaxul, gigafaxul, terafaxul etc...

The Expofaxul group

The main number in this group is the expofaxul = 200!1, or 200^199^198^197^196^195^....^3^2. This is the last number in my naming system that can be written out in full in power tower form in the entire universe, because the next number, the kiloexpofaxul = expofaxul!1 = expofaxul^(expofaxul-1)^(expofaxul-2)^...^4^3^2, cannot be written out in exponent form even if you could use the entire observable universe and you could write a digit in every single cubic planck length. There is also the megaexpofaxul, gigaexpofaxul etc.

The Tetrofaxul group

The main number in this group is the tetrofaxul = 200!2, or 200^^199^^198^^197^^196^^195^^....^^3^^2. Then there is the kilotetrofaxul = tetrofaxul!1 = tetrofaxul  ^^(tetrofaxul-1)^^(tetrofaxul-2)^^...^^4^^3^^2. There is also the megatetrofaxul , gigatetrofaxul etc.

The Pentofaxul group

The main number in this group is the pentofaxul = 200!2, or 200^^^199^^^198^^^197^^^196^^^195^^^....^^^3^^^2. Then there is the kilopentofaxul = pentofaxul!1 = pentofaxul^^^(pentofaxul-1)^^^(pentofaxul-2)^^^...^^^4^^^3^^^2. There is also the megapentofaxul , gigapentofaxul etc.

This naming system will continue with the Hexofaxul group, the Heptofaxul group, the Octofaxul group and so on.

The Hyperfaxul group

Finally there is the hyperfaxul = 200!200 or 200![1]. This is also equal to a Ducenfaxul, but the extensions do not continue like this. There is the kilohyperfaxul = hyperfaxul![1], megahyperfaxul = kilohyperfaxul![1] etc. Then there is the grand hyperfaxul, the hyperfaxulth term in the sequence starting hyperfaxul, kilohyperfaxul, megahyperfaxul etc., of course, there is also the grand kilohyperfaxul etc. 

Major Faxul Group

The Giaxul group

This group contains numbers like the giaxul = 200![200], then the kilogiaxul = giaxul![200] etc, with the usual names including the grand –giaxul group as well as the usual –giaxul lot.

Then, there is the giabixul = 200![200,200], with all the extensions (kilogiabixul etc), the giatrixul = 200![200,200,200], the giaquaxul = 200![200,200,200,200] (pronounced gia-quazzle) and so on. It is worth taking note of the size of these numbers, for example, take the giaxul. It is far, far larger than Graham's number, and even g(200) in the sequence.

The Hugexul group

This group is the limit of linear arrays. It contains the hugexul = 200![200(1)200]  as its main number, and all the usual extensions. There is also a new extension as well for the hugexul: the superior hugexul = 200![200(1)200,200]. There will also be the superior kilohugexul = superior hugexul![200(1)200,200]. The prefixes should always be ordered x-superior y-grand z-hugexul, with x, y, and z representing the further prefixes you could add to the prefixes (ie trisuperior), and so order does not matter, and therefore they are (sort of) communicative.

Then there is the hugebixul = 200![200(1)200(1)200], the hugetrixul = 200![200(1)200(1)200(1)200] and the hugequaxul = 200![200(1)200(1)200(1)200(1)200] and so on. For comparison, the Meameamealokkapoowa oompa fits around about the hugebixul mark (i think). The meameamealokkapoowa oompa is the largest Bowerism made in BEAF.

The Enormaxul group

This group begins with the enormaxul = 200![200(2)200], and then there are all of the usual extensions, including the superior enormaxul = 200![200(2)200,200] and all the superior extensions. Then there is the enormabixul = 200![200(2)200(2)200], the enormatrixul = 200![200(2)200(2)200(2)200] and the enormaquaxul = 200![200(2)200(2)200(2)200(2)200]

The Destruxul group

This group begins with the destruxul = 200![200(200)200]. Then there is the great destruxul = 200![200(200)200(200)200], the bigreat destruxul = 200![200(200)200(200)200] and so on. Then, there is the destrucbixul = 200![200([200(200)200])200], the destructrixul = 200![200([200([200(200)200])200])200] and the destrucquaxul = 200![200([200([200([200(200)200])200])200])200] etc.

The Extremexul group

In this group there is the extremexul = 200![1(1)[2200,200,200,200]], the extremebixul = 200![1(1)[2200,200,200,200,200]], the extremetrixul = 200![1(1)[2200,200,200,200,200,200]] and the extremequaxul = 200![1(1)[2200,200,200,200,200,200,200]]. Of course, with all of these numbers you can still get things like the kiloextremebixul and the grand extremequaxul, with the same rules as before. You can also use the vast prefix to change the final bracket to have an extra ([200]) seperator in a similar way to destruxul, destrucbixul, destructrixul...

The Gigantixul group

This group starts with the gigantixul = 200![1(1)[3200,200,200]], the gigantibixul = 200![1(1)[3200,200,200,200]], the gigantitrixul = 200![1(1)[3200,200,200,200,200]] and the gigantiquaxul = 200![1(1)[3200,200,200,200,200,200]].

Mammoth Faxul Group

The Nucleaxul group

This group takes a big step up into the furthest reaches of hyperfactorial notation. The nucleaxul = 200![[200200]]. Then, there are the usual names: The nucleabixul = 200![[[200200]200]], the nucleatrixul = 200![[[[200200]200]200]] and the nucleaquaxul = 200![[[[[200200]200]200]200]].


BIGG stands for Bewilderingly Incomprehensibly Ginormous Googolism (in case of doubt, just pronounce it as you would just "big"). The BIGG = 200?. There are no prefixes for the BIGG. This number is on a scale far beyond any other googolism I have ever made before. It is, as the name suggests, BIG. VERY BIG.

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