I have used the sum operator in many of my previous posts and I’m going to use it even more in the future. I’ve introduced bits and pieces about this notation and some of its properties but this information is scattered across many posts. For these reasons, I decided to dedicate a special post to the sum operator where I show you the most important details about it.

[Read more…]## Natural Numbers and Arithmetic: Intuition

Welcome to the third post from my series on numbers and arithmetic. In the previous two posts, I gave an overview of **real numbers** (and their main subsets), as well as the main operations between them. And in the rest of the series, we’re going to build all these concepts from scratch. Well, the focus in today’s post is the most basic subset of the real numbers: the **natural numbers**.

*This post is part of my series* Numbers, Arithmetic, and the Physical World.

## What are Mathematical Functions?

The topic of today’s post is **mathematical functions**. Functions are such a fundamental part of mathematics that you’re certain to encounter them almost everywhere.

Recently, I started a small series on numbers and arithmetic, in order to begin exploring the intuition of basic mathematical concepts that most of us take for granted. And these concepts themselves are the building blocks of more advanced concepts, including more advanced concepts in probability theory.

But to fully understand them, we also need to know the details and intuition of some general mathematical tools which we’re going to rely on along the way. Well, functions are first in line!

[Read more…]## Arithmetic Properties: A Comprehensive Breakdown

Welcome to the second post from my series on numbers and arithmetic. As a sort of continuation to the introductory post, here I want to talk about the most important properties of arithmetic operations.

*This post is part of my series* Numbers, Arithmetic, and the Physical World.

## Numbers, Arithmetic, and the Physical World (Series)

Hi, everyone! Today’s post is the introduction to a new mini-series on numbers and arithmetic.

In this series, I’m going to take you back to some elementary math concepts from your childhood. I want you to get a good intuition about fundamental mathematical objects which we use in pretty much everything else we do in math. Namely, the objects called **numbers**.

Besides numbers themselves, I want to focus on the intuition behind the most common operations with numbers: addition, subtraction, multiplication, division, exponentiation, roots, and logarithms. The field concerned with these operations is called **arithmetic **and is one of the fundamental fields in mathematics.