The introduction of numbers is an integral part of mathematics and its development, though not all numbers have been treated the same throughout history. The number 0 was not considered a number for much of human history until renowned mathematician al-Khwarizmi introduced it as one.
Similarly, number 1 was met with skepticism from generations of ancient mathematicians — especially in influential regions such as Greece and Alexandria. Notably, mathematician Euclid was among those who did not acknowledge the number 1 as a number and instead saw it as something entirely different conceptually. Euclid’s contributions to mathematics were vast, with geometry perhaps his most significant legacy. As such, Euclid is the driving force behind what we now call the very fundamental pillar of mathematics.
In fact, this is because the concept of numbers in mathematics has evolved, developed, complicated, and changed over time. Everything in mathematics has very clear and precise definitions, except for some axioms, and these definitions are made in the most specific way possible. Usually, these definitions are clear enough to be written in the language of logic.
Let’s take equality as an example, and let’s take the set equality to show an example. We know that sets with the same elements are equal sets, and this definition seems…
