What is real analysis?

Isaac Newton

In 1665, Isaac Newton invented calculus. In 1727, he died a virgin. Now it's your turn.

Don't worry; the path is well-paved. Since Newton, other mathematicians have distilled the invention calculus into an area of study called real analysis.

This may sound like serious business. It's not.

What are the main ideas of real analysis?

Analysis deals a lot with infinity and its associated funny business.

Fortunately, you don't have to be a genius who can see into the fourth dimension to understand infinity. Instead, we explore infinity the same way a 4 year old does: by asking annoying questions.

For example, if your little brother asks whether 1n\frac{1}{n} gets smaller than this 🤏 you can always throw a big nn at him and win. That's how we know it gets infinitely small.