Strongly continuous family of operators

Okay, imagine you have a bunch of machines in your room, and you want to make them do different things at different times. But you don't want them to suddenly stop or change what they're doing all of a sudden, because that might be confusing.

So, you want to make sure that when you switch from one thing to another, it happens really smoothly, like a car accelerating slowly instead of suddenly jerking forward.

This is kind of like what a "strongly continuous family of operators" means in math. It's a fancy way of saying that you have a bunch of operations (or machines, if you will) that you're going to use in a certain order, and you want them to have a smooth transition from one to the next.

In other words, you want to make sure that if you tweak one thing a bit (like changing the order of the machines), it won't suddenly mess up everything else.

So, when we talk about a "strongly continuous family of operators" in math, we're saying that we have a bunch of operations that are "connected" in a smooth way, so that we can use them together without suddenly changing everything.