The Greatest Integer Function

Ceil x = -floor(-x)

Amazing

Who came from williams prime formula?

You made my day great

Thank you

Imagine the greatest integer function as a step(which is also what its graph looks like). If you input a number in the function it would tell you what integer floor you crossed to get to that number. E.g- [2.9] -> the function will tell us we just crossed floor number 2. [0.6]-> This will tell that you just crossed the ground floor that is 0th floor. [-1.4]-> This will tell that you have crossed the first floor of the basement that is -1 and you are heading towards the ground floor. Remember that the building is infinitely tall both below and above the ground! :)

Could somebody explain why f(x) = [[x-8]] has nonremovable discontinuities at each integer k? I think I have an intuition why based on the graph, but what exactly can I plug in to realize this?

All those are calling Sir are Indians.

I think you forgot the most important part of the problem here.
[[-2.3]] = -3
Some people might think it's 2.

Well explained thank you

Great sir 👍

Thanks ❤️

gracias amigo, el pendejo de mi profesor no se supo explicar con la tarea que nos dejo y tuve que encontrar la respuesta aquí, por lo que agradezco tu explicación y ayuda

fck math

The best and precise explanation Sir! Thank you very much!

Thanks but can i understand the concept they were going with like why they made a function like this

It's basically mathematical snakes and ladders. One thing I found out was that it is helpful to remember that f(x) is still y. The problem I had while learning this was treating the greatest value as a value of X on a number line instead of a value of Y. No one explains this and just assumes you got that part. I think it is helpful to teach so that the full structure of the equation is full understood.