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I've come up with a new number naming system that will probably never get into popular use but is in my opinion a definate improvement over the existing English number naming system when it comes to large numbers. Especially since the existing system allows the same number name in many cases to mean drastically different things in only slightly different dialects of the same language. If you like my system, and plan to publish any work in which it is more important that the large number names be unambiguous than that they be familliar, please use this system if you like it so that it can get to be well known. Since it is a new system, be sure to include enough information for people to translate the word names you use into digit form if they choose to take the time to do so, even if that information is only in an apendix or glossary at the end of your work. I'm not claiming any kind of copyrights on this system, but rather releasing it into the public domain where it belongs. I know there will be those who see ways to improve on my system and think that since it's new, they might just as well use their improved version instead of my original. That's okay with me, but I would like to discourage it for the following reason. I also can see ways of improving my own system, but have chosen to leave them out in favor of keeping a form that is similar enough to the old system that it may feel somewhat natural to people who are comfortable with the older English number names. A living language will change and evolve, but a certain amount of stability is needed in order for it to be practical. If you introduce changes to this new number naming system, then anyone learning your modified version of this naming system is just as likely to want to make further modifications, and in the end nothing will have been accomplished. On the other hand, if you use my system as-is, and encourage others to do likewise, then the system may gain acceptance as a new standard and we will together have brought an improved number naming system into common usage. By the way, if you are unfamilliar with the what I mean about large number names not having consistant meanings in the English language, then you probably have no real need for this new naming system. If that is the case, consider using it anyway because it will still allow you to say large number names with fewer syllables and write or type them with fewer letters.

This is a base one million number naming system and works much like scientific notation except that it gives names to large numbers rather than simply a numeric exponent and of course that it is based on powers of 1000000 rather than a base 10 exponent. For example, 1000000000000000000000000000000000000000000000000000000 = 1.0*10^54 = 1.0E+54 = 1000000^9 = one onilin.

The commonly known number one googol is a 1 with 100 zeros after it, which is 1.0*10^100 = 1.0E+100 = 10000*1000000^16 = ten tau dekihexilin. Although my system is base 1000000, those who are accustomed to the old base 1000000 system of million, milliard, billion, billard, and so on, may find my my system a bit awkward at first since for example one billiard under that system becomes one tau bilin under my system, but this will shorten more number names than it will lengthen as for example what was two billion five hundred tirty six milliard four hundred twenty two million one hundred twenty nine thousand three hundred fourty seven under that system will be two bilin five hun tirty six tau four hun twenty two milin one hun twenty nine tau three hun fourty seven, in this new system. By the way, in the system currently used in the United States of America at the time of this writing, that same number is two trillion five hundred tirty six billion four hundred twenty two million one hundred twenty nine thousand three hundred fourty seven, so you can see that the naming system in use at this time becomes ambiguous when you consider that the name values are not agreed upon internationally. This is one reason I made sure that my new number names are different enough not to be easily confused with the old names.

Okay, here's how the new number naming system works....

Groups of 2 digits are named the old way. I had worked out an alternative that I felt would be better, but since the numbers from 1 to 99 are used so much it is unlikely that many people would be willing to re-learn how to say their names. For this reason, I have decided to simply let those names be dictated by common usage rather than suggest an alternative.

For three digit numbers, I suggest only one small change. That is, to use "hun" rather than "hundred" since this change could be easily adapted and would make lone number names that part of a number name quicker and easier to type or say, especially when used repeatedly as part of any unreasonably large named number or in a list of numbers. The last two digits in the group would be named in the usual way.

The name of 1000 in the new system is tau, rather than "thousand" since this shorter form would save time and effort when dealing with very large numbers, and would be easy to learn as a replacement for the old name.

For groups of six digits, each group of six would be treated as two groups of three, with the first group representing a multiple of tau.

As the next nine groups of six digits are added to higher order positions beyond the lowest order group, they would be given the following names: milin, bilin, drilin, terilin, quilin, hexilin, sepilin, okilin, onilin. Each sucessive name represents a power of one milin. For example, one milin is a one followed by six zeros, and a quilin is a one followed by five groups of six zeros or in other words it is one milin to the fifth power. These names have been chosen for their similarity to the old English names, as well for their simplicity. I have also attempted to choose names that will mesh well with languages other than English, to the best of my ability to do so. The zeroeth group is named ilin, but is not intended to be used without a prefix. This is important though, since the 'il' prefix is used as a sort of place holder like a zero in the exponents of very large numbers, but I will explain this more later.

The tenth group of six digits is prefixed with dek, so that after onilin comes dekilin, and after dekilin comes dekmilin. This makes a dekilin the first sixty digit number.

Groups of 600 digits are sub-divided into ten groups of sixty digits each. As the next nine groups of sixty digits are added to higher order positions beyond the lowest order group, they would each be givin a 'tens group' prefix as follows: dek, bidek, dridek, teridek, quidek, hexidek, sepidek, okidek, onidek. This designated the tens place of the exponent so each sucessive name formed by prefixing "ilin" with one of these forms represents a power of one dekilin. The ones place prefix of the exponent can be inserted to form any two digit power of 1000000. For example, a 1 followed by 3 groups of six zeros is a drilin, while a 1 followed by 73 groups of six zeros would be a sepidekdrilin.

Groups of 6000 digits are sub-divided into ten groups of 600 digits each. As the next nine groups of 600 digits are added to higher order positions beyond the lowest order group, they would each be givin a 'huns group' prefix as follows: cen, bicen, dricen, tericen, quicen, hexicen, sepicen, okicen, onicen. These represent powers of one cenilin, which in turn is the 100th power of one milin. For example, a 1 followed by 30 groups of six zeros is a dridekilin, while a 1 followed by 730 groups of six zeros would be a sepicendridekilin.

Groups of 60000 digits are sub-divided into ten groups of 6000 digits each. As the next nine groups of 6000 digits are added to higher order positions beyond the lowest order group, they would each be givin a 'taus group' prefix as follows: mil, bil, dril, teril, quil, hexil, sepil, okil, onil. For example, a 1 followed by 300 groups of six zeros is a dricenlin, while a 1 followed by 7300 groups of six zeros would be a sepildricenlin. As mentioned earlier, the 'il' prefix is a place holder for zeros in the exponent in the power of 1000000 represented by a number name. It is implied for the lowest order tau group name and not expressed unless such a group is further prepended by a higher order grouping prefix. If the lowest order tau group is to be given an additional prefix as part of a larger group that it is contained within, then it mush first be prepended explicity by the otherwise implied 'il' prefix. This construction process allows the tau group orders to double as place holders creating an unlimited capacity and allowing the naming system to represent any finite rational number.

Groups of 600000 digits are sub-divided into ten groups of 60000 digits each. As the next nine groups of 60000 digits are added to higher order positions beyond the lowest order group, they would each be prepended by a 'tens group' prefix as follows: dek, bidek, dridek, teridek, quidek, hexidek, sepidek, okidek, onidek. For example, a 1 followed by 3000 groups of six zeros is a drililin, while a 1 followed by 73000 groups of six zeros would be a sepidekdrililin.

A 'tens group' prefix, in addition to being prepended to successive higher order groups of sixty digits and sixty tau digits, is also prepended to successive higher order groups of sixty milin digits, sixty tau milin digits, sixty bilin digits, sixty tau bilin digits, sixty drilin digits, sixty tau drilin digits, sixty terilin digits, sixty tau terilin digits, sixty quilin digits, etc., in a regular cycle.

Likewise, a 'huns group' prefix, in addition to being prepended to successive higher order groups of six hun digits, is also prepended to groups of six hun tau digits, six hun milin digits, six hun tau milin digits, six hun bilin digits, six hun tau bilin digits, six hun drilin digits, six hun tau drilin digits, six hun terilin digits, six hun tau terilin digits, six hun quilin digits, etc., in a regular cycle.

Finally, a 'taus group' prefix is prepended to not olny successive higher order groups of six tau digits, but also to successive groups of six milin digits, six tau milin digits, six bilin digits, six tau bilin digits, six drilin digits, six tau drilin digits, six terilin digits, six tau terilin digits, six quilin digits, etc., in a regular cycle.

Here is a list of the first 22 place value names in successive order, from the ones place, to the mililins place:

ones
tens
huns
taus
ten taus
hun taus
milins
ten milins
hun milins
tau milins
ten tau milins
hun tau milins
bilins
ten bilins
hun bilins
tau bilins
ten tau bilins
hun tau bilins
drilins
ten drilins
hun drilins
tau drilins
	

For a list of the first 6001 place value names, go to: oocities.com/technozeus/mililin.html

Using those place values, any number can be represented in the range of zero to one less than a dekililin.

Here are some simple descriptions of some of the number names beyond mililin:

1 mililin = 1 with 1000 groups of 6 zeros after it, or 1000000 to the 1000th power.
1 milmilin = 1000000 to the 1001st power.
1 milbilin = 1000000 to the 1002nd power.
1 mildrilin = 1000000 to the 1003rd power.
1 milterilin = 1000000 to the 1004th power.

1 bimililin = 1 with 2000 groups of 6 zeros after it, or 1000000 to the 2000th power.

1 drimililin = 1000000 to the 3000th power.

1 terimililin = 1000000 to the 4000th power.

1 onimilonicenonidekonilin = 1000000 to the 9999th power.

1 dekmililin = 1 with 10000 groups of 6 zeros after it, or 1000000 to the 10000th power.

1 bidekmililin = 1000000 to the 20000th power.

1 dridekmililin = 1000000 to the 30000th power.

1 teridekmililin = 1000000 to the 40000th power.

1 bidekililin = 1 with 6 dekilin zeros after it, or one milin to the dekilinth power.

1 quidekililin = one milin to the bidekquilinth power.

1 okidekililin = one milin to the teridekilinth power.

1 cenmilililin = one milin to the quidekmililinth power.

1 mililililin = one milin to the quicenmililinth power.

1 dekmililililin = one milin to the quimilililinth power.

1 cenmilililililin = one milin to the quidekmililililinth power.

1 mililililililin = one milin to the quicenmililililinth power.

	

For more examples, go to: oocities.com/technozeus/example-numbers.html

Okay, now some people may wonder about the logic involved in the naming of such large numbers, so let me clarify a few things.

Milin is a 1 followed by a group of 6 zeros. Bilin is a 1 followed by 2 groups of 6 zeros. Drilin is a 1 followed by 3 groups of 6 zeros. Terilin is a 1 followed by 4 groups of 6 zeros. Quilin is a 1 followed by 5 groups of 6 zeros. Hexilin is a 1 followed by 6 groups of 6 zeros. Sepilin is a 1 followed by 7 groups of 6 zeros. Okilin is a 1 followed by 8 groups of 6 zeros. Onilin is a 1 followed by 9 groups of 6 zeros. Dekilin is a 1 followed by 10 groups of 6 zeros. Dekmilin is a 1 followed by 11 groups of 6 zeros. Dekbilin is a 1 followed by 12 groups of 6 zeros. This pattern continues up to oncenondekonilin which would be a 1 followed by 999 groups of 6 zeros.

The initial prefix is an indicator of rank. When you get to large enough numbers, the number of zeros after the one is itself a large number. For this reason, I will list the number of zeros after the one for the following number names. For mililin the number of zeros would be a 1 followed by 1 group of 3 zeros. For bililin the number of zeros would be a 1 followed by 2 groups of 3 zeros. For drililin the number of zeros would be a 1 followed by 3 groups of 3 zeros. For terililin the number of zeros would be a 1 followed by 4 groups of 3 zeros. For quililin the number of zeros would be a 1 followed by 5 groups of 3 zeros. For hexililin the number of zeros would be a 1 followed by 6 groups of 3 zeros. For sepililin the number of zeros would be a 1 followed by 7 groups of 3 zeros. For okililin the number of zeros would be a 1 followed by 8 groups of 3 zeros. For onililin the number of zeros would be a 1 followed by 9 groups of 3 zeros. For dekililin the number of zeros would be a 1 followed by 10 groups of 3 zeros. For dekmililin the number of zeros would be a 1 followed by 11 groups of 3 zeros. This pattern continues up to oncenondekonililin for which the number of zeros would be a 1 followed by 999 groups of 3 zeros.

This exponential extension of the initial prefix is repeated for successive larger groupings. I will now list the number of zeros after the one for the next order of number names. For milililin the number of zeros would be a 1 followed by 1 group of 3000 zeros. For bilililin the number of zeros would be a 1 followed by 2 groups of 3000 zeros. For drilililin the number of zeros would be a 1 followed by 3 groups of 3000 zeros. For terilililin the number of zeros would be a 1 followed by 4 groups of 3000 zeros. For quilililin the number of zeros would be a 1 followed by 5 groups of 3000 zeros. For hexilililin the number of zeros would be a 1 followed by 6 groups of 3000 zeros. For sepilililin the number of zeros would be a 1 followed by 7 groups of 3000 zeros. For okilililin the number of zeros would be a 1 followed by 8 groups of 3000 zeros. For onilililin the number of zeros would be a 1 followed by 9 groups of 3000 zeros. For dekilililin the number of zeros would be a 1 followed by 10 groups of 3000 zeros. For dekmililin the number of zeros would be a 1 followed by 11 groups of 3000 zeros. For dekbililin the number of zeros would be a 1 followed by 12 groups of 3000 zeros. For dekdrililin the number of zeros would be a 1 followed by 13 groups of 3000 zeros. This pattern continues up to oncenondekonilililin for which the number of zeros would be a 1 followed by 999 groups of 3000 zeros. Notice that I'm not saying that oncenondekonilililin represents a 1 followed by 999 groups of 3000 zeros, but rather that oncenondekonilililin represents a 1 followed by tau tercenondekonililin zeros.

For larger orders of magnitude the power of 10, or number of zeros following the one, continues to increase exponentially. For terililililin the number of zeros after the 1 would be a 1 followed by 4 groups of 3 000000 zeros. For hexilililililin the number of zeros after the 1 would be a 1 followed by 6 group of 3000 000000 zeros. For okililililililin the number of zeros after the 1 would be a 1 followed by 8 group of 3 000000 000000 zeros, or in other words, okililililililin represents a 1 followed by 10 to the four-bilinth power groups of six zeros.

Donald A. Kronos, PhD.

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