What does [x] means in mathematics ?

In summary, the conversation discusses the use of the notation [x] in mathematics, which is often used to represent the greatest integer function. The function returns the largest integer less than or equal to x. The conversation also mentions the alternative notation \lfloor x \rfloor for the same function. The conversation concludes by highlighting the importance of context and the need for flexibility in using symbols in mathematics.
  • #1
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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 ?
 
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  • #2
[] 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.
 
  • #3
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. :)
 
  • #4
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.
 
  • #5
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.
 

What does the symbol "∑" mean in mathematics?

The symbol "∑" is known as the summation symbol in mathematics. It represents the sum of a series of numbers or expressions. For example, "∑x" would mean the sum of all values of x in a given series.

What does "√" mean in mathematics?

The symbol "√" is known as the square root symbol in mathematics. It represents the inverse operation of squaring a number. For example, √9 would mean the number that when squared, results in 9.

What does the notation "f(x)" mean in mathematics?

The notation "f(x)" is used to represent a function in mathematics. It indicates that the variable x is being operated on by the function f. For example, f(x) = 2x would mean that the function f takes in an input of x and outputs 2 times that value.

What does "π" represent in mathematics?

"π" is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159 and is commonly used in calculations involving circles and spheres.

What does the symbol "≤" mean in mathematics?

The symbol "≤" represents the less than or equal to relation in mathematics. It is used to compare two values and indicate that one value is either less than or equal to the other. For example, 2 ≤ 5 would mean that 2 is less than or equal to 5.

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