what does [x] means in mathematics ? i have found [x]= "the greatest integer <=x " is this true ? then, what will be the answer of of ..... [3],[1.5],[-1.5],[3.5] i am trying to answer, please correct me [3]=3 [1.5]=1 [-1.5]=-1 [3.5]=3 are these correct ?
[] meaning greatest integer is a common use of the [], but it can vary.You should check whatever book your problems are from, they should define what they mean by the notation. If it is the greatest integer function, then "[-1.5]=-1" isn't correct. You want the greatest integer less than or equal to -1.5, so it can't be -1 as -1.5<-1.
So, in what way is the defintion for [tex][ x ][/tex] you've given different from [tex]\lfloor x \rfloor [/tex] ? - also given to be the symbol for the floor function, which matches the definition you gave. None, AFAIK, just a "who's the author" thing. IMO, it's just a bad nomen confusum problem. I've also seen it used in characteristic functions. Somebody ought to pick one use, and pitch the rest.... :) and penalize deviating authors 10 points for misuse. :)
Rubbish, Jim: there are far too few symbols possible and far too meanings that need to be conveyed. Context makes it clear what is going on.
Uniqe and fossilized use of symbols is counter-productive of developing flexibility of the mind. It is the definition AT HAND that matters, and if the chosen notation is convenient for its purpose.