User blog:Edwin Shade/A Number Naming System Perhaps Beyond Saibian or Bower's !

For most Googologists, Graham's number's is seen as a benchmark to beat when creating their own notations. It came as a surprise to me then, when I saw that Jonathan Bower's naming system is only effective in naming integers to about $$10\uparrow \uparrow 6$$ !

Granted, that is a large number, but no where near Graham's number. Trying to piggyback on Bower's or Saibain's naming system will do little if we are to reach the goal of creating a naming system for all numbers between 1 and graham's number, inclusive. (Or at least reaching a higher number than has been reached with pre-existing naming schemes. We need to create something new for this.

So here begins the fun.

From $$1$$ to $$1,0000^{1,0000}$$
First let me establish this new naming system will be based on powers of 10,000, instead of the traditional 1,000's, similar to Knuth's "-yllion" system. This is done due to the efficiency of grouping zeroes into 4's instead of 3's, and due to the fact that the current grouping system has some problems. For instance, take a billion, or $$10^{9}$$. The word for a billion contains the prefix for two, so we should expect it to mean the second power of a thousand, but instead it refers to the third power of a thousand. This discrepancy is continued as long as we use the -illion system, with a centillion meaning $$10^{303}$$ instead of $$10^{300}$$ as the prefix "centi-" would seem to mean.

So to avoid the confusion that would result if I tried to accurately rename the current system, I have decided to use a system in which zeros are grouped by 4's, and hence we will need to name powers of 1,0000, or $$10^{4}$$.

To begin with, $$1,0000^{1}$$ is simply called a "myr", which is the word myriad truncated by three letters. $$1,0000^{2}$$ is called a "bimyr", which conjoins a myr and the prefix for two together.

If you have a number such as 1,2345,6789 you would pronounce it as "one bimyr, twenty-three hundred forty-five myr, sixty-seven hundred eighty-nine". Again, the concept is very similar to the "-yllion" system at this point.

$$1,0000^{3}$$ is called a "trimyr", which conjoins the prefix for three with the base myr.

$$1,0000^{4}$$ is called a "quamyr", which conjoins a customized prefix for the number four with the base myr. I could has used 'quadri-' instead, but it wastes fewer letters to abbreviate that to 'qua-'. Likewise, the prefix for five, 'quinta-', has been shortened to just 'qui-'. A quimyr therefore would be equal to $$1,0000^{5}$$.

$$1,0000^{6}$$ is called a "simyr", which is derived from the English word for six and the base myr. I again could have just called it a "sexmyr", but it doesn't roll off the tongue as easily as simyr does; therefore I changed the prefix.

$$1,0000^{7}$$ is called a "vemyr", which takes the 've' from the English word for 7 and conjoins it with myr. This has been done instead using an abbreviated form of the current prefix for seven, "septe-" -> "se", because se sounds too similar to si, so it may cause confusion.

$$1,0000^{8}$$ is called an "ocmyr", which is an abbreviated form of the prefix for 8 joined with the word myr.

$$1,0000^{9}$$ is called a "nomyr", which is an abbreviated form of the prefix for 9 joined with the word myr.

So, to recap; 'un' means 1, 'bi' 2, 'tri' 3, 'qua' 4, 'qui' 5, 'si' 6, 've' 7, 'oc' 8, and 'no' 9. With these prefixes we can name all powers of 1,0000 from $$1,0000^{1}$$ to $$1,0000^{9}$$. To name $$1,0000^{10}$$ requires us to have a prefix for 10. Let us use 'de', or a shortened form of the prefix 'deci-'. Now we can name $$1,0000^{10}$$ as a "decimyr".

Here is where my naming system begins to diverge more noticeably from the traditional -illion system. To name $$1,0000^{11}$$ I am going to put the prefix for one, 'un', after the prefix for 10, 'de'. This is different, because if you were naming for example a number like $$10^{36}$$ you would call it a "undecillion". It is unclear though why the one's-prefix should come before the ten's-prefix, when that is not at all how numbers work when writing them down. So to correct matter, the prefixes come in the relative order you would expect them to, with the one's prefix being after the ten's prefix, so that "deunmyr" means $$1,0000^{11}$$.

'Twe-' should be used as a prefix for 20, 'thir-' for 30, 'for-' for 40, 'fi-' for 50, 'li-' for 60, (pronounced 'lee'), 'qi-' for 70, 'ei-' for 80 and 'ni' for 90, (pronounced 'nigh'). The prefixes for 60 and 70 have been adapted from the Chinese names for 6 and 7.

$$1,0000^{12}$$ is a "debimyr".

$$1,0000^{13}$$ is a "detrimyr".

$$1,0000^{14}$$ is a "dequamyr".

$$1,0000^{15}$$ is a "dequimyr".

$$1,0000^{16}$$ is a "desimyr".

$$1,0000^{17}$$ is a "devemyr".

$$1,0000^{18}$$ is a "deocmyr".

$$1,0000^{19}$$ is a "denomyr".

$$1,0000^{20}$$ is a "twemyr".

$$1,0000^{25}$$ is a "twequimyr".

$$1,0000^{30}$$ is a "thirmyr".

$$1,0000^{35}$$ is a "thirquimyr".

$$1,0000^{40}$$ is a "formyr".

$$1,0000^{45}$$ is a "forquimyr".

$$1,0000^{50}$$ is a "fifmyr".

$$1,0000^{60}$$ is a "limyr".

$$1,0000^{70}$$ is a "qimyr".

$$1,0000^{80}$$ is an "eimyr".

$$1,0000^{90}$$ is a "nimyr".

$$1,0000^{99}$$ is a "ninomyr".

Finally, we introduce the prefix for 100, 'cen-', which when combined with any of the already formed prefixes allows us to list the powers of 1,0000 from $$1,0000^{1}$$ to $$1,0000^{9999}$$.

$$1,0000^{100}$$ is a "cenmyr".

$$1,0000^{150}$$ is a "cefifmyr".

$$1,0000^{200}$$ is a "bicenmyr".

$$1,0000^{300}$$ is a "tricenmyr".

$$1,0000^{400}$$ is a "quacenmyr".

$$1,0000^{500}$$ is a "quicenmyr".

$$1,0000^{600}$$ is a "sicenmyr".

$$1,0000^{700}$$ is a "vecemyr".

$$1,0000^{800}$$ is a "occemyr".

$$1,0000^{900}$$ is a "nocemyr".

$$1,0000^{1000}$$ is a "decemyr".

$$1,0000^{2000}$$ is a "twecemyr".

$$1,0000^{4000}$$ is a "forcemyr".

$$1,0000^{6000}$$ is a "licemyr".

$$1,0000^{8000}$$ is an "eicemyr".

$$1,0000^{9999}$$ is a "ninoceninomyr".

[W.I.P.]