After All, Is Zero a Number?

If we researched the number zero in depth, we would have material to write a complete book. Here we will only make a small essay addressing some curious and interesting aspects.

In general, zero refers to the idea of ​​emptiness. Modern mathematics of set theory presents zero as the empty set, but if that same zero is placed inside the set, it becomes an element of that mathematical set. So what is the logic of zero? To understand trivia from scratch, we have to look at it in multiple contexts.

Number systems are a set of rules that deal with basic operations like addition, multiplication, subtraction and division and are studied in arithmetic. Basically, a number in arithmetic is the result obtained when measuring a quantity, or quantity, for example: the number of students in a classroom.

When measuring a magnitude it will not make sense to do it in something that does not exist, therefore, in this case, there will be no need to represent the void, that is, zero will not exist.

The question arises in the act of expressing the quantities, which will sometimes be spoken, sometimes written. Then comes Numbering.

Of course, when it comes to speaking, one must bear in mind that, as far as numbers are concerned, these were no exception to the process of merging and evolving languages ​​and idioms. But originally the term unit is very common.

In practical terms, if, for example, we have a plate on each side, then we say that there are four plates on the table, or four units.

A very simple and popular numbering system is that of small dashes:

🦆= |

🦆🦆= |⎺

🦆🦆🦆= |⎺|

But this is not the system used by arithmetic, that is, to express numbers it uses two formal ways: through words and through written symbols.

For spoken numeration, arithmetic establishes a paradigm, that is, a rule that makes the way of expressing numbers comfortable. Here comes the collection concept:

• collection of first-order units: one, two, three, four, five, six, seven, eight, nine. With this collection, the units are counted one by one.
• collection of second-order units: from quantity nine onwards, the units default to ten, which makes up the collection of ten. Quantities between tens are formed by combining first-order terms with units.
• uma coleção de dez dezenas representa a centena, esta é a unidade da terceira ordem. E assim sucessivamente.
• a collection of ten tens represents the hundred, this is the third order unit. And so on.

For written numbering, arithmetic provides a collection of signs called digits. Each sign corresponds to a term from the collection of first order unit terms.

Note that the zero appears there, so it represents a digit in arithmetic. The purpose of zero will be to allow you to write all the numbers because in each order you cannot count beyond nine.

On the other hand, set theory had a great influence on the development of mathematics, so much so that it served as the basis for the formalization of various topics and then zero came to be considered as an element of numerical sets or enumeration, it is said that zero belongs to set of real numbers, or belongs to the set of integers. Thus, it is common in algebra and analytic geometry texts that zero is established as the so-called neutral element of the addition operation.