Semi-continuity

Okay, imagine you have a toy car and you want to know how fast it can go. You press a button and the car starts moving forward. Now, while the car is moving, you start pressing down on the button more and more. Sometimes, when you press down more, the car will go faster, but sometimes it will stay at the same speed.

This is kind of like semi-continuity, which is a way to talk about how things change when you change something else. In the case of the car, you're changing how much you press the button, and you're seeing how the car responds.

In math, we talk about functions, which are kind of like toy cars. A function takes in some number (like how much you're pressing the button), and then it spits out another number (like how fast the car is going). Just like the car, sometimes the function will change a lot when you change the input, and sometimes it will stay the same.

So, semi-continuity is a way to talk about functions and how they behave when you change the input a little bit. If you have a semi-continuous function, it means that if you change the input a little bit, the output will only change a little too. Just like with the car, sometimes a small change in the input will cause a big change in the output, but sometimes it will only cause a small change.

So, that's what semi-continuity means. It's a way to talk about how functions behave when you change the input a little bit, and whether or not they change a lot or just a little.