Glossary

Below is a list of terms related to numerals, number systems and the community. Note that most of the terms related to Argam numerals are Valerian-derived and not seen in any of De Vlieger's published work.

A

Additive definition
Numerals that are defined by adding two (or more) numbers according to the rules of the numeral system. For example, the Mayan numerals are additive, and the value of each numeral is defined as adding one for each dot and five for each bar.
**Alpha-totative** - In a given number base, the alpha totatives are the divisors of the number one above the base. The alpha number in its base is always written as 11, but it represents different values depending on which base it is.

**Alphanumeric Transdecimal Digits** - A proposal for numerals for bases up to 36. The letters A through Z are used to denote values ranging from ten to thirty-five. Called "computerese" among the base analyst community.

**Alternate form** - Also called "alts", numberforms that are valid, though are not the most conventional.

**Amarian form** (argam) - Former name for alternate argam numberforms devised by Dozenalism that isn't currently Valerian-Canon (see Valerian form).

**Apostrophe Notation** - A notation proposed to express numbers in any number system with only unicode characters that are easily accessible.

**Argam** /AHR-gam/ - (also spelled as "arqam", singular form: "ragam"/"raqam") A set of transdecimal numbers invented by Michael De Vlieger used to express numbers in larger number bases.

* Argam Ajamyse - The set of Argam numerals, as of 1986.
* Argam Arimaxa - The set of Argam numerals, as of the 1990s.
* Rykami Argam - The set of Argam numerals, as of 2007/2008.
* Argam-Kinoctove - The Argam numerals, specifically trimmed to Digit-359, to express numbers in Base 360. "kinoctove" is the ismarragam (name) for Digit-360, meaning

5
⋅
8
⋅
9

{\displaystyle 5\cdot8\cdot9}

. It is also the sixth superior highly composite number.
* Argam-Kinsevoctove - The Argam numerals, specifically trimmed to Digit-2,519, to express numbers in Base 2,520. "kinsevoctove" is the ismarragam for Digit-2,520, meaning

5
⋅
7
⋅
8
⋅
9

{\displaystyle 5\cdot7\cdot8\cdot9}

. It is also the seventh superior highly composite number.
* Argam-Sevoctovess - The Argam numerals, specifically trimmed to Digit-5,039, to express numbers in Base 5,040. "sevoctovess" is the ismarragam for Digit-5,040, meaning

7
⋅
8
⋅
9
⋅
10

{\displaystyle 7\cdot8\cdot9\cdot10}

. It is also the eighth superior highly composite number.

**Argam Fifteen'd** (or Argam 15'd) - A slang term from the DBB2 community, meaning "tricked", as the argam numeral representing fifteen bears the name "trick". E.g. "We Argam Fifteen'd Billy into giving us the font files"

**Assumed Canon** - See "canon".

B

**Base** - Number systems usually revolve around a number and its perfect powers to represent numbers. That number is called the base.

* Most humans use decimal (base 10) to count and to represent different numbers. On the other hand, binary (base 2) and hexadecimal (base 16) are much preferred by computers.

**Base Analyst Community** (BAC) - A community devoted to the study of the properties and use of different number bases and systems.

**Bootgam** - Derives from a portmanteau of "bootleg" and Argam. A slang term originating from the DBB2 community for numeral proposals that use the same logic behind Argam without making any significant improvement.

**Bracketed C** (argam) - The letter C used in stacked letter primes where an extra stroke, resembling a right bracket ), is added to the letter C itself. A notable example is digit-103 "cobe ().

C

**Canon** (canonical numerals) - Meaning the current numberforms preferred by the creator of a numeral proposal, if there are alternate numberforms. In argam, this means the numberform is preferred by De Vlieger or Dozenalism.

* Assumed Canon - Numbers that have never appeared in canonical work, and could only be predicted by observing the patterns of canonical numerals. The Argam-540 reference page features several assumed Icarine canonical argam numerals for numbers that have never appeared in his work.
* **Icarine-Canon** (argam) - Canonical argam numberforms preferred by De Vlieger.
* **Valerian-Canon** (argam) - Canonical argam numberforms preferred by Dozenalism.

**Chemical Element Primes** (argam) - CEP for short, prime numbers that are based on two stacked letters from the symbols of the chemical elements, which includes most prime numbers from 89 through 647 inclusively. Subset of the stacked letter primes (see below).

**CM** - Short for content moderator, a user who has the rights to make changes to protected pages and templates.

**Connector form** (Argam ismarragam) - Suffixes from ismarragam (argam numeral names) are modified when used in the middle of a name instead. The modified forms are called connector forms. For example, digit-245 "eff**in**kin" derive from digit-49 "eff**ent**" and the prefix for 5 "kin", for 5 × 49. "-ent" is the suffix for squared numbers, and "-in-" is the connector form.

**Computerese** - See Alphanumeric transdecimal digits.

D

**Daughter Numeral** - A numeral that has elements (strokes, curls etc.) that directly derive from another numeral. If the original numeral experiences change, daughter numerals are very likely to change as well. For example, in Argam, digit-38 "dax" () is a daughter numeral of digit-19 "ax" ().

**DBB2** - Short for *Different Base Blocks II*, an online community devoted to reworking the children's show *Numberblocks* into different bases and number systems.

**Decimal**

1. The positional number system with ten as its base. Used by the vast majority of humans in daily life.
2. Non-integers that the fractional part is expressed according to its expansion according to a specific base (place value).

**Digit** - A number, usually an integer that can be used alone (e.g. 3) or in combinations (e.g. 37) to represent numerical quanities.

**Divisor** - A number *a* is a divisor of *b* if *a* divides *b* with no remainder left.

**Dozenal** - The positional number system with twelve as its base. Often advocated for its many patterns and high divisibility, while being a human-scale base.

**Dozenalist** - A person is fluent and prefers the use of dozenal (base twelve).

**DozensOnline** - The Tapatalk forum about numerals, number systems, systems of measure and mathematics.

**DSA** - Short for the Dozenal Society of America, an organization based in the United States that advocates the usage of base twelve.

**DSGB** - Short for the Dozenal Society of Great Britain, an organization based in Great Britain that advocates the usage of base twelve.

* **Semidivisor** - A number *a* is a semidivisor of *b* if *a* divides a power of *b* with no remainder left. Alternatively, *a* is a semidivisor of *b* if the fraction 1/*a* terminates in base *b.* For example, 4 is a semidivisor of 10, as 100 is divisible by 4.

**Dym Cid** - A slang term originating from the Learningblocks community meaning "dumb kid". The term is usually pronounced "dumb kid", although it could also be pronounced "dim sid" or "dime sid".

E

**Element** - Groups of lines, curves or other strokes in a numeral.

**Eleven** - Usually equated as the number two more than nine, but in some proposals the number written "11" in any bases bear this name.

**Even** - A property for whole numbers that they are divisible by two with no remainders left. For even bases like decimal, a number is even if the last digit is even. For odd bases like pentadecimal, a number is even if the sum of its digits is even.

* **Singly even** - A number that has only one factor of two, i.e. numbers divisible by 2 but not by 4. For example, 22 is singly even because 22÷4=5.5.
* **Doubly even** - A number that has exactly two factors of 2, and as such is divisible by 4 but not by 8. For example, 36 is doubly even because 36÷4=9 and 36÷8=4.5.
* **Triply even** - A number that has exactly three factors of 2, and as such is divisible by 8 but not by 16.
* **2-order** (of an integer) - How many times the integer can be divided by 2 without any remainders. This is equivalent to the amount of twos in its prime factorization. For example, the 2-order of 96 is 5, as dividing 96 by 2 five times yields 3, which is not divisible by 2. The 2-order of any odd number is 0.

F

**Factor** - See divisor.

**Factorization** - Breaking down of an integer into a pair (or more) of factors. For example,

# 12
2
×
6

{\displaystyle 12 = 2 \times 6}

,

# 12
3
×
4

{\displaystyle 12 = 3 \times 4}

,

# 12
1
×
12

{\displaystyle 12 = 1 \times 12}

and

# 12
2
×
2
×
3

{\displaystyle 12 = 2 \times 2 \times 3}

are all factorizations of 12. Factorization most commonly refers to the prime factorization of a number, in this case

# 12
2
×
2
×
3

{\displaystyle 12 = 2 \times 2 \times 3}

.

H

**Half-Integer** - Numbers in the form

n

1
2

{\displaystyle n + \frac{1}{2}}

, where

n

{\displaystyle n}

 is an integer For example, 3.5, 6.5, and -18.5 are all half-integers, while 0.05, 1.55 and 9.75 are not.

**Human Scale** (bases) - Usually defined as positional number systems with radix of six through sixteen inclusive. Human scale bases have a good amount of digits for human computation (the average human should be able to easily recognize and manipulate those digits, and basic arithmetic would not be a hassle), and that large numbers have a reasonable amount of digits.

**Humphrey point** - The semicolon that replaces the decimal dot (decimal separator) for numbers represented in dozenal (base twelve). For example, in dozenal, one half could be written as 0;6.

I

**Improper Numeral** - For numbers written in base

b

{\displaystyle b}

, the improper numerals are digits with value greater than

b

{\displaystyle b}

. For example, 186 = 226 = 1410, where the digit 8 used is considered "improper". These can be useful when doing arithmetic as carrying could be done at a later stage or that the number of digits could be "reduced" (as in if one were to multiply 127 by 134 by hand, treating the two numbers as  and  reduces the amount of digits to handle.)

**Integer** - (also called a "whole number") A number that can be written without a fractional component (e.g. 14, 6, -23).

**Ismarragam** (argam) - The names of the Argam numerals. "ism." for short.

**Irregular Form** (argam) - A numberform, or the ismarragam (name) for a singular ragam, that does not follow the general pattern.

**IUPAC Prime Scheme** (argam) - A proposal for larger prime argam numerals according to the IUPAC naming method for superheavy elements. A major con to this is that is specific to a certain base and defeats the purpose of the argam numerals being base-neutral.

M

**Misalian base-naming system** - A base-neutral system for naming bases devised by YouTuber jan Misali, created due to his observation that the term "base 10" can be ambigious, because its value changes depending on the base used to define the term. It relies on a few root values (1-13, 16, 17, 36, 100) and other bases multiplicatively defined, with prime bases being additive due to having no usable divisor pairs.

**Multiplicative Definition** - Numerals, or other things related to numbers that are designed according to a factorization of the numbers, commonly the prime factorization. Examples include the Argam numerals or the aforementioned Misalian base-naming system.

N

**Natural number** - A positive integer. It is debatable whether 0 counts as a natural number, it usually depends on the situation it is used in. (also called counting numbers, positive integers or non-negative integers, which the latter two used depending on whether zero counts)

**Number System** - A systematic way to represent different numerical quantities.

**Number Systems Wiki** - Affiliated wiki about the analysis of number bases or other systems. NSW for short.

**Numberform** - The shape of the numeral, as two numerals in the same system denoting the same quantity can be represented differently.

**Numeral** - A figure, or a group of figures that denotes a numerical quantity. For example, the ten figures {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} are the set of Hindu-Arabic Numerals used by the vast majority of humans.

**Numeral Box** - An imaginary "bounding box" that serves as a guideline to the simplicity of the numerals.

**Numeral Proposal** - A proposal for representing numbers that is not generally universally-accepted (yet).

**Numeral Set** - A set of numerals.

**Numeralpedia** - This wiki, which focuses on number symbols and the cultural history of numbers.

O

**Odd** - A number property for whole numbers opposite to the property of even. A number is odd if it *cannot* be divided by 2, i.e. division by 2 leaves a remainder (of 1).

**Omega** - In a given number base, the number exactly one below the base. It represents the digit with the highest value.

P

**Parity** - The property of a number whether it's odd or even.

**Prime** - A number property for whole numbers that can only be divided by 1 and themselves. The first 10 prime numbers (in decimal) are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

**Prime factorization** - A factorization of a number using only prime numbers. There can be more than one of the same prime in the factorization. By the fundamental theorem of arithmetic, each integer has exactly one distinct prime factorization. For example,

# 2520
2
×
2
×
2
×
3
×
3
×
5
×
7

{\displaystyle 2520 = 2 \times 2 \times 2 \times 3 \times 3 \times 5 \times 7}

. Prime numbers are their own prime factorization.

Q

**Quadrate** - A number divisible by 4.

R

**Radical** - A graphical part of a numeral, often simplified, that conveys a certain value to be multiplied. For a full list of radicals in argam, please visit this page.

**Radix** - The base of a positional number system. Same as "base", but the specific term is useful in some places where base would be ambigious (e.g. radix point, radix economy).

**Ragam** (argam) - Also spelt "raqam", the singular form of "argam".

S

**Single-Digit significant number** - A number composed of a single digit followed by any number of zeroes. That is, any number that could be written as

x
⋅

10
y

{\displaystyle x \cdot 10^y}

(for any base), where

x

{\displaystyle x}

 and

y

{\displaystyle y}

 are integers and

x

{\displaystyle x}

 is a positive integer smaller than the base. For example, 3, 20, 500 and 9,000,000 are single-digit significant (in decimal), while 2.2, 75 and 110 are not.

**Sketchbook of Numbers** (argam)- Also known as rykami-argam, the sketchbook De Vlieger produced between 2007 and 2008 that studied the expansion of the argam beyond 120 numerals as well as large number bases.

**Stacked-Letter prime** (argam) - SLP for short, prime argam numerals that are based on two (or rarely more) stacked letters of the English alphabet.

Stroke - A mark made by drawing a pen, pencil, or paintbrush in one direction across paper or canvas

T

**Ten** - Usually equated as the number one more than nine, but in some proposals the number written "10" in any bases bear this name.

**TM** - Short for thread moderator, a user on this wiki who has the right moderate any posting (messages, posts, comments) by editing and deleting them.

**Transdecimal Bases** - Number bases that require the use of digits with value exceeding 9. This term is usually referred to positional number systems only, though in some cases it may also include balanced or negative bases. Transdecimal derives from *trans-*, meaning "beyond", and decimal (base ten).

**Transdecimal Digit** - A digit used in bases larger than decimal (i.e. digits with value larger than nine). The vast majority of numeral proposals are for transdecimal bases. For example, in computers, the transdecimal digits {A, B, C, D, E, F} are used to represent the values of ten through fifteen for hexadecimal.

**Trine** (property) - an integer divisible by three. 39 is trine because 39÷3=13 with no remainder.

* **nontrine** - an integer not divisible by three. 31 is nontrine because 31÷3=10 with remainder 1.
* **overtrine** - an integer that is 1 greater than a trine number, and as such has a remainder of 1 when divided by 3 (numbers congruent to 1 modulo 3). 43 is overtrine because 43÷3=14 with remainder 1.
* **undertrine** - an integer that is 1 less than a trine number, and as such has a remainder of 2 when divided by 3 (numbers congruent to 2 modulo 3). 47 is undertrine because 47÷3=15 with remainder 2.
* **trinality** (also trinarity or trinity) - the property of being trine, undertrine or overtrine. Corresponding term to "parity" for odd/even numbers.

**Totative** - In a given number base, a totative is an integer such that its greatest common divisor with the base is 1, that is, coprime to the base. Use of this term (rather than *coprime*) is favored in places where many numbers are likely to be compared to a single number, mostly in number bases.

* **Alpha-totative** - In a given number base, an Alpha totative is the number exactly one above the base.
* **Omega-totative** - In a given number base, an Omega totative is the number exactly one below the base.
* **Semitotative** - In a given number base, a semitotative is an integer that has at least one common prime factor with the base and at least one prime factor not shared with the base. For example, 6 is a semitotative in bases 8, 10, 14, 16.

**Twin Prime** - Prime numbers that differ by two. For example, 29 is part of the {29, 31} twin prime pair, while 37 is not a twin prime, as 35 and 39 are both composite.

V

**Valerian Form** - A variant of De Vlieger's argam numerals by Dozenalism (founder of this wiki). The variant aims to simplify the current canonical argam and extend the set up to 5,040 numerals. The name comes from *Valerie*, Dozenalism's fictitious younger sister, whose name comes from *valentine*.

**Valerian-Derived Canon** - VDC for short, Canonical argam numerals (see "canon") that are Valerian numberforms, i.e. those created by Dozenalism.

**Value** - The numerical amount denoted by a numeral (or a mathematical expression).

**Verbal representation** (of a number) - How the number is represented verbally. For example, the English verbal representation of the number 59 is "fifty-nine".