What is to be done when the finite ordered sequence of counters is exhausted, yet more objects remain to be matched?

r or a placeholder. The same is true with the number systems based on the principle of addition, in these systems there is no requirement of the concept of zero.

eaving empty space where the missing coefficients of particular order were to be found. Hence they would write a number such as [1; 6] for lets say 3606. But this did not solve the problem completely. In copy or reading these spaces could be overlooked, and particularly when two or more space were to be given it could be confused with one space. But since the Babylonians has the base as 6o the need for writing numbers with zero in between arises on a very few occasions than it does in the number system with base 10. In case of the sexagesimal numeration only in 59 integers below 3600 this arises; as compared to 917 cease in the base 10 system \cite{boyer}. The Babylonian zero is the first zero to arrive on the scene. To denote absence of a coefficient of a particular order in their representation of the number, the Babylonians used a special sign [after fourth century BCE], which is the a cuneiform sign looking like a double oblique chevron. The Mayans developed their positional system with base 20, but they were not consistent with the use of the powers of the base after the third position \cite{uni2} pg 670. The Mayans understood the concept of zero sign, but they did not have its operational usability due to their inconsistent positional system. In case of the Babylonians it was never understood as a number synonymous with empty and never corresponded to the meaning of null quantity. So we see that in spite of having the notion of zero the Mayans and teh Babylonians did not get much further in this. The Mayan and the Babylonian zeros are as given in the figure.

1.The idea of attaching each basic figure with signs removed from intuitive associations.2. The idea of a positional number system, in which the value of a number depends on its position in the representation.3. The idea of a full operational zero, filling the empty spaces of missing units and at the same time having the meaning of a null number.

- Distinct representation of one to nine numbers, which had forms unrelated to the number they represented.
- Discovery of the place value system.
- Invention of the concept of zero.

- The nine numerals were only used in accordance to addition principle for analytical combinations using numerals higher than or equal to ten, the notation was very basic and limited to numbers below 100,000.
- Place value system was only used with sanskrit names for numbers.
- Zero was only used orally.