floor and ceiling functions

 I asked Google the question "Are answers with floor and ceiling functions mathematical ?". The answer is "Yes".

I have a few expressions which may work well and can be considered mathematical. They however need floor and ceiling functions. 

So, all in all I do have valid mathematical statements. And they use floor or ceiling functions. The results are demonstrated with the help of Wolfram Alpha. Thank you, Wolfram Alpha.

Have a nice day !!