Zero-start and one-start

We can count numbers in two manners. Either by relating start of a-unit (number zero onwards) or by relating physical a- units (in which end of a-unit is counted as '1'). Hor line ____ is a-unit! A line has a start to it, a length to it and a state to it (liner, curve, or a combination of both. Let us analyse a straight line alone). A straight line can be divided into several 'equal parts' and 'each part' can be regarded a-unit. Further, each merged "number-unit" comprises 'a number' and 'a-unit'. For example a"9 cm" is "a number-unit 9" and "a length unit" cm. Nine number units are shown below graphically!

0......1......2......3......4......5......6......7......8...zero-start

____ ____ ____ ____ ____ ____ ____ ____ ____ --->9 a-units

....1......2......3.......4......5......6......7......8......9... ---> 'Usual count' relates each unit in 'one to one position' (one-start).

Obviously it is one unit more than a digital count!

You can extend above logic to zero start 2D square matrix positions, which relates y and x ordinates and each of these have merged properties of pair-numbers. These area-units are bound by a vertical unit-y and an equal horizontal unit-x in a 2D square matrix. In a 2D matrix there are several merged 'yx' units!

You can also extend this logic to zero-start 3D cube-matrix positions, which relates z, y and x ordinates. It relates 3D-properties of "merged 3-digit numbers". Each 'cube unit' is bound by three equal 'square area-units' yz, yx and zx!

Vedic manner relates "before-units count" (either linear, or area or a cube unit), which gives us a precise 'digital number sense'. A start-unit has 'no before unit of it' and said condition 'no' is zero. Second unit has obviously 'one' unit before it. Third unit has 'two' before-units so on! This is principle of using 'zero-start number count', which is much older than 'Vedic period' in India!

However, users have consistently preferred physical 'one to one' count (one-start) , which is also explained in above graph. A Verbal explanation of these facts will confuse an ordinary user of counts. So both are concurrently explained (graphically)! Obviously a difference of one-unit exists in between a zero-start and a one-start, which is ekdhika (one more than...) explained in Vedic Mathematics. More manners to relate 'ekadhika' exist, which also applies to all Vedic sutras!

Vedic Mathematics used 'zero-start number counts' and people preferred 'one-start'!

A concerned "paradox" did exist ever since ancient Indian Mathematics grew as a public utility knowledge, which continues even now! A great possibility to apply numbers (by relating positive numbers alone) had disappeared along with Vedic Mathematics, which is now re-emerging!

A Vedic sutra "ekadhikena" (one more than...) reveals these facts in a book published by followers of shree Jagadguru Sankaracarya (1884-1960) . Some mathematicians openly claim that 'contents of "Vedic Methematics" are not-scientific'. "Truth will emerge victor". Let us wait!