The New Base Ten
New Theory and Proposal of a new mathematical numbering system which is still "base ten", but, removes a logical error in the Arabic system's use of "0".
Abstract: During the millennial celebration from year 1999 to 2000, most everyone except for one or two news anchors and a few guests said that year "2000" is the ushering in of the first year of the new 3rd millennium. (Just as their "logic" stated year "1000" was the start of the 2nd millennium.) "Well," anchor, Peter Jennings, pointed out, "that is wrong." Jennings had the wisdom (and guts) to point out the fact, some people know, that every number ending in 0 (zero) defines the last number, or end, of the last 10 (ten), or 100, or 1000, (ending in two zeros, three zeros - respectively). It doesn't start the beginning of the next "number series". Example: the two digit, 10 (ten), doesn't start the teen series; the three digit, 100, doesn't start the 2nd hundred series. 11 (eleven) does, and 101 does in these examples. Another example: 1970 is still the last year of the sixties decade. It doesn't start the seventies decade. 1971 does. Therefore, it is proposed not to add a "digit" to a number until the number reaches its proper amount, series, or denomination, if you will. Accordingly, this will redefine the use of zero (or delete it from the ten numeric symbols, and imply recreating a new symbol for the tenth numeric symbol - so as not to get 0 (zero) confused in this new system with the Arabic old system). For instance, (for the time being until a real numeric symbol can be created for usage), let's use the letter "T" for the tenth numeric symbol instead of 0 (zero). The first ten counting numbers would then be: 1,2,3,4,5,6,7,8,9,T. "Wait a minute," one would say, "what about going or counting from positive integers to the negative numbers? You must pass through zero' first, before 1 goes to -1." Well, since zero is really nothing, it doesn't really define a "number" (defined in this paper as a real amount being positive or negative). To represent that "transitional point" between the entire universe of positive fractional numbers and the negative fractional numbers, I'll let the "non numeric", "zero", be used only once: for the absolute point interface between the positive numeric realm and the negative one. So see, zero or "0" need not really be "used" except to define this once only, exact point transition. For the purpose of definition, here, let's not create an eleventh numeric symbol, but simply designate the name of this interface point as "zero", yes, spelled out in letters (not a number), as "zero". Now whether or not one wants to call zero a "number" and give it a legitimate symbol, (even as an eleventh symbol), is really not the main point of this paper. Whether or not doing this, it doesn't defeat the numbering system (the new base ten, I'll call it), that I am proposing herein and below.
Now here is the first thousand and one numbers as these would be in this new logical numbering system (as opposed to the system now used):
The first set of ten: 1 2 3 4 5 6 7 8 9 T. The second set of ten: 11 12 13 14 15 16 17 18 19 1T. Continuing to one thousand and one: 21 22 23 24 25 26 27 28 29 2T, 31 32..39 3T, 41 42..49 4T, 51 52..59 5T, 61 62..69 6T, 71 72..79 7T, 81 82..89 8T, 91 92..99 9T (one hundred), 1T1 (One hundred one), 1T2...1T9 1TT (one hundred ten), 111 112.119 11T, 121 122...129 12T, 131...13T, 141..14T,.. and so on to 191.19T (two hundred), 2T1 (two hundred one),..2T9 2TT (two hundred ten), 211..21T, 221...22T,.. and so on to 29T (three hundred), 3T1..you continue to 999 99T (one thousand), 1TT1 (one thousand one), ..and so on you continue to number through the thousands, etc.
Big note of importance: notice the tenth symbol: it still retains its proper one digit status! The twentieth number does not get a "2" in its first digit place. That is reserved for the first number of the "twenty" series, i.e. the twenty first number. Same goes with the thirties through the nineties. Note the 100th symbol does not get three digits.
The first three digit number properly belongs to the one hundred and first number, not the one hundredth one. Three digit numbers should not properly show until you are past one hundred. Three digit numbers (the first one hundred of them), represent the second one hundred in this counting system. This same logic goes in the thousands designation, tens of thousands, and so on.
The T is a unique symbol, in a way, in that it is a "control or border digit" - telling the counter that a new series of numbers is about to occur, or, a whole new digit is about to be added on (when T is prefixed by one or more 9's).
All functions and equations can be performed using these numbers since the result is a number defined here. But for simplicity of example, I show only some integers or whole numbers. For example, let's do multiplication. Though this takes getting use to. (The multiplication tables for old numbers with zero will look different and be substituted with results in the new numbering with "T"). One example: (old system: 2 X 40 = 80). New system: 2 X 3T = 7T. Two times 3 something equals 7, a prime number? Looks funny, but it really isn't a 2 X 3 = 7. 3T is thirty ten (the old forty). The result: 7T is seventy ten (the old eighty). Two times (forty) is (eighty).
But despite this use of the tenth digit (to get adjusted to), I propose this new numbering, one day, be in global use to replace the illogical one in use today.