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# Dates mathematics, Chapter 1 Do you like dates or mathematics? We know what dates and mathematics are, but we do not know yet how and when they could be done in one recipe? In this text I shall answer this question and, so, bringing into light one of the most beautiful work pieces in mathematics and natural sciences. The revelation came to me about one year ago when I started again to reflect on numbers that are very common in the Islamic realm. I wrote then down a few lines and left it to time. At the closure of 2016 and the beginning of 2017 I thought it was necessary to go ahead with that (idea) as it may help in my career as a scientist and academic researcher. The courage I had in this work was due to my engagement in basic research since 2000 as ESKAS-scholarship holder at the University of Basel and more recently (2015) in school mathematics for one year with my niece.

In this mathematics discovery I intuited that numbers could be ordered according to their value and, thus, could be handled mathematically with such order note rather than their true value or amount note. On doing so, elegant equations, beautiful patterns and new applications might be possible. The commencement was truly thrilling and exciting. It threw green light that everything should be all right.

1- The ordinal numbering system

The numbers in the ordinal numbering system can be written as such:

…., I9-, I8-, I7-, I6-, I5-, I4-, I3-, I2-, I1, I2, I3, I4, I5, I6, I7, I8, I9, ….

These ordinal numbers match the following numbers in the common mathematics:

…., – 8, – 7, – 6, – 5, – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, ….

2- Equations to derive ordinal numbers

Ix = x – 1 ………………………………… (1); when x is positive

Ix- = – (x – 1) ………………………….. (1-1); when x is negative

Ix/y = (x/y) – 1 ………………………. (2); when x/y is positive, and x/y > 1

Ix/y- = – ((x/y) – 1) ……………………. (2-1); when x/y is negative and |x/y| > 1

3- Simple mathematical operations with ordinal whole numbers (In)

3.1: Additions and subtractions

Addition rule:

Ix + Iy = Ix+y-1 ……………… (3); when x and y are positive

Ix- + Iy- = I(x+y-1)- ……………… (3); when x and y are negative

Ix + Iy- = I(x-y+1) ………… (3-1); when x > |y| or x = |y|

Ix- + Iy = I(-x+y-1) ………… (3-2); when |x|> y

Subtraction rule:

Ix – Iy = Ix + Iy- ………………. Use either (3-1) or (3-2)

I(x-) – Iy- = Ix- + Iy ………… Use either (3-1) or (3-2)

3.2: Multiplication and division

Multiplication rule:

Ix . Iy = I(x.y) – (x+y-2) ………………. (4); when x and y are positive

Ix- . Iy- = I(-x.-y) – (x+y-2) ………………. (4-1); when x and y are negative

Ix- . Iy = I((x.y) – (x+y-2))- ………………. (4-2); when either x or y is negative

Division rule:

Iz/Ix = I(z+x-2)/x-1 ………………….. (5), when x and y are both positive or both negative

Iz-/Ix = I((z+x-2)/x-1))- ………………….. (5-1), when either x or y is negative

Examples:

1) I1 = 1 – 1 = 0

2) I2 = 2 – 1 = 1

3) I2- = – (2 – 1) = – 1

4) I1 + I2 = I1+2-1 = I2 = 1

5) I2 + I2- = I2-2+1 = I1 = 0

6) I3 – I2- = I3 + I2 = I3+2-1 = I4 = 3

7) I2 . I2 = I4-4+2 = I2 = 1

8) I2/I2 = I(2+2-2)/2-1 = I2/1 = I2 = 1

9) I1/I1 = I(1+1-2)/1-1 = I0/0 (not known)

10) I2/I3 = I(2+3-2)/3-1 = I3/2 = 3/2 -1 = 1/2

N.B. Intellectual and perpetuations rights of this material are protected property for the author. Please, in case of any questions or interest in this material refer to the author. Author’s e-mail address: elsherbinimustafa@gmail.com

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