Does a proof exist for the reflexive property (x=x)?

Question

I have read an article suggesting that proofs or explanations do not exist for some very basic properties in math, including "$x$ is equal to $x$." A preliminary online search did not yield a satisfactory answer.

Does a mathematical proof or other explanation exist for the reflexive property in mathematics?

Answer 1

A relation $R$ is reflexive if it satisfies $x R x$ for all $x$. It is up to you to show that a particular relation is reflexive.

That having been said, mathematics is bootstrapped by assumptions. These assumptions are called axioms. Long story short: you have to start from somewhere, and hence you have to assume something.

Answer 2

That is one of the axioms of equality. An axiom in mathematics is a rule that helps you pin down what you're talking about - it defines the system you're using. Equality has to be reflexive because otherwise it wouldn't be equality.