Mathematics

An Elegant Proof That 1 + 1 = 2

And 2 + 2 = 4 and so on

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1 + 1 = 2. 2 + 2 = 4. 2000 + 24 = 2024. At first glance, they are just simple additions that even a 6 year-old kid would be able to compute. Now what if I told you that mathematicians in the past have developed concrete axioms to rigorously prove that 1 + 1 is indeed equal to 2. Keep reading and you will be able to impress your friends and family!

Mathematics is about rigor and elegance, and we are going to see just that in this article.

Peano Axioms

Peano and his family (source)

Presented by the 19th-century mathematician Giuseppe Peano, the Peano axioms are a set of axioms for the natural numbers in mathematical logic. Generally, axioms are statements taken to be true, upon which further reasoning nd arguments are built. Think of them as the bedrock for all of mathematics.

Before we can fully appreciate the rigor behind why 1 + 1 = 2, we first have to understand what the equality sign really means. We don’t want to have any room for confusion or contradiction.