Zero vs Nothing
It is very important to understand the different between zero and nothing. Many years ago there was no zero. Also, though people knew the concept nothing, there was no mathematical notation for it.
The ancient number systems such as Egyptians had no zero. They had a unary system or an additive system, in which they used repetition of one symbol to represent any number. Two was two of the symbols for one. For ten, the number of symbols were getting out of hand. Therefore, they introduced a new symbol for ten. Twenty was two of the symbol for ten. Similarly, they had different symbols for hundred, thousand and so on. Hence, they did not have a need of zero. Ancient Greeks, who learned the fundamentals of their math from the Egyptians, had a different number system with nine symbols for each digit from one to nine. They also did not have zero. Their number system did not feature a place holder as did the Babylonian. The abacus has a tendency to suggest the positional model. However this concept was developed by Babylonians. In the position number system, numbers are put in columns, and there is a unit column, a tens’ column, a hundreds’ column, and so on. For example, 243 will be II IIII III. They left a space for zero. In some numbers such as 2001 where there are two zeros, it is impossible to keep a bigger space. Eventually, the Babylonians introduced a place holder. By 130 AD, Ptolemy the Greek astronomer used the Babylonian number system, but with zero represented by a circle. In later ages, Hindus invented zero, and it came into use as a number. Hindu zero symbol came with a meaning of ‘nothing’.
There is indeed difference between zero and nothing. Zero has a numerical value of ‘0’, but nothing is an abstract definition. Number ‘zero’ is very strange. It is neither positive nor negative. Nothing is the absence of something. Therefore, it does not have any value.
Let us consider this sentence. “I had two apples, and I gave you two”. It results with ‘zero apples’ or ‘nothing’ with me. Hence, someone can argue that zero and nothing have the same meaning.
Let’s take another example. Set is a collection of well defined objects. Let A= {0} and B be a null set, in which we have nothing inside it. Therefore, the set B={}. The two sets A and B are not equal. The set A is described as a set with one element since zero is a number, but B has no elements. Therefore, zero and nothing is not the same.
Another difference between zero and nothing is zero has a measurable value under the position number system, which we are using in modern mathematics. But ‘nothing’ does not have any positional value. Zero is a relative term. Absence of a zero can make a huge difference.
There are few rules in arithmetic involving zero. Addition or subtraction of zero to a number does not affect the value of the number. (i.e. a+0=a, a0=a). if we multiply any number by zero, the value will be zero, and if any number raised to the power of zero is one (i.e. a^{0}=1). However, we cannot divide a number by zero and cannot take the zeroth root of a number.
What’s the difference between Zero and Nothing? • ‘Zero’ is a number while ‘nothing’ is a concept. • ‘Zero’ has numerical position value, while ‘nothing’ is not. • ‘Zero’ has its own properties in arithmetic, while nothing has any such properties.

Ivonne Sanchez says
In the story for using the zero, what about the Mayans? They used a zero too.