Draft:Tridecimal

Tridecimal (also known as Tredecimal, Triskedecimal, Baker’s Dozenal, of Base 13) is a positional numeral system that uses thirteen as its base. When writing in tridecimal, different symbols can be used such as X, E, T, following the precedent set by undecimal, A, B, C following the precedent set by hexadecimal, or some people use X, Y, Z.

Ways to Count
Although several systems with tridecimal do not have a verbal counterpart to express numbers, there have been proposed methods for counting in Baker’s Dozenal. With this method, the numbers from 0 to 11 are said the same, 12 becomes ‘dozen’ and 13 becomes ‘baker’s dozen’. After this, numbers are added onto the end until Base-13 20 is reached, where it becomes ‘baker’s twenty’. This pattern of substituting the Base-10 counterparts and having ‘tenty’, ‘eleventy’, and ‘dozenty’ substituted for those who do not have Base-10 counterparts. After this, to represent Base-13 100, the term ‘one batch’ is used similar to how a gross is used in Base-12. When Base-13 200 is reached, the term used is ‘two batch’ rather than ‘two batches.’ No verbal representation is given after number dozen batch baker’s dozenty dozen or Base-10, 2352.

In Mathematics
The Conway Base 13 Function is a function that is discontinuous everywhere but contains all of the points between any two points with a non-zero distance. This function uses tridecimal by adding digits for Base-10 10, 11, and 12 as ‘+’, ‘-’, and ‘.’. The function uses these symbols to see if a number is well-formed in tridecimal and to figure the output of a specific number.

In Fiction
In The Hitchhiker’s Guide to the Galaxy, Douglas Adams suggests that the solution of 42 is received by multiplying 6 and 9. People have found that this is true if counting is done in tridecimal, the statement is true. Adams, in an online discussion, was asked about this and he claimed that the statement was nonsense and that he does not make jokes in Base-13.