Algebra is our first real encounter with the mind-bending concept of infinity.

We see it in a simple solution like 'x > 5'. This is not one answer; it is an infinite set of answers.

We see it in the graph of a line, which is a collection of an infinite number of points extending forever in both directions.

We see it in an asymptote, where a graph approaches a line for an infinite distance without ever touching it.

The mathematician Georg Cantor developed a rigorous algebra for dealing with different *sizes* of infinity in his work on set theory.

He proved the mind-blowing fact that some infinities are bigger than others.

The infinity of real numbers is demonstrably 'larger' than the infinity of integers.

Algebra gives us the tools to reason about and manipulate this concept that our minds can't fully visualize.

It allows us to treat infinity not as a vague, mystical idea, but as a concrete mathematical object with its own rules.

It is our first step into a larger, more profound mathematical universe.