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Recalling addition, the atom of operations


Addition is one of the oldest mathematical operations. It is the most simple, natural, and obvious operation to perform. It is about registering the increased quantity of something, upon (more) acquisition of that thing. Addition reflects the mathematical interpretation of the joy of owning more and more!
The operation addition is so uniquely foundational that the other three operations can be expressed in terms of addition (we will discover this over the three volumes of books on operations). It is for this reason that we consider addition to be like the atom of operations. Recall that atoms in chemistry refer to extremely small particles that combine to form molecules; atoms are the smallest independent/stable unit of matter.
Collecting, gathering, or aggregating things of all sorts is one of the distinctive characteristics of humans and many animals too. There is more to this among humans – we like to specifically assess the quantity of collection every time things of the same kind are brought in possession.    
To know the exact quantity in a collection, we count them. Do we need to count every time we collect more of the thing to know the total quantity in the collection? For example, if there were 5 apples in your house and you bring another 7 apples home. What are the possible ways of knowing the new total number of apples?
The two possible ways are:

  1. Count the total number of apples again, that is, count the apples starting first, second … till twelfth.
  2. Find a way to connect/combine the numbers - 5 apples and 7 apples - to get the total (we know the count of apples at home and the count of apples that were brought)

While counting all the apples again is definitely a way to know the total quantity of apples, recounting every time more apples become part of collection would be tedious, and prone to mistakes, especially when the number of things become bigger. Finding a way of combining smaller quantities of similar things to get the total quantity of the combined things is the way to go.
Addition is just that – a method to find the combined count of things we put together; an operation on the quantity of things we are combining. The symbol used for representing the operation addition is ‘+’ and is called ‘plus’. There is more to the name and symbol, which we will come across later in the book.
Let us learn about addition. Clearly, we must start with revising what we know about counting. Counting and addition are very closely linked. We will explore the exact connection between the two in this book.

Summary

Counting is the process of finding the quantity of ‘similar things’ of whatever we have chosen to quantify – the ‘unit of counting’ – in a given collection of things. We count using ordinal number names and we state the amount of quantity using cardinal number names. Don’t worry, ordinal and cardinal numbers are discussed in the Learning Outcome 2.


Excerpted from the book ‘Foundations of Addition (Mathematics as a language)’ by Sandeep Srivastava and Saloni Srivastava