In order to have the rigorous proof of these properties, we need a rigorous definition of what a limit is. And we're not doing that in this tutorial. We'll do that in the tutorial on the epsilon delta definition of limits. But most of these should be fairly intuitive. And they're very helpful for simplifying limit problems in the future. So let's say we know that the limit of some function f of x as x approaches c is equal to capital L. And let's say that we also know that the limit of some other function, let's say g of x as x approaches c, is equal to capital M. Now, given that, what would be the limit of f of x plus g of x as x approaches c? Well, and you could look at this visually.