Influence of non-standard analysis

Okay kiddo, let's try to understand the influence of non-standard analysis together!

So, have you ever heard of numbers like infinity or infinitesimal? They're really big or really small numbers that we can't really work with in our normal math rules, but sometimes we need to use them in science or engineering.

That's where non-standard analysis comes in. It's a special way of doing math that lets us talk about these weird numbers without breaking our regular math rules.

Basically, non-standard analysis uses something called "hyperreal numbers" that are kinda like regular numbers, but also kinda like infinity and infinitesimal. They let us do things like take limits and derivatives, which are key parts of math and science.

Some people think that non-standard analysis has had a big influence on those fields, because it lets us talk about things we couldn't before. It's like a new tool in our toolbox!

But don't worry too much about it if it doesn't make complete sense yet. Non-standard analysis is pretty advanced math, and even grown-ups sometimes have trouble with it. Just remember that it's a cool new way of doing math that helps us understand the world around us better!