Is there a mathematical expression to use only the integer result of division?

Question

For example, if I'm doing division, and I just want the integer value, how do I express that mathematically? E.g., 10/3 = 3 instead of 3.33333. Thanks for any help you can give me.

Answer 1

Use brackets,
[10/3] = 3
The brackets are notation for the greatest integer function.
[x] means the greatest integer less than or equal to x.
[10/3] = [3.33333...] = 3 since the greatest integer less than or equal to 3.33333... is 3

Answer 2

There is a mathematical function called the Greatest Integer Value function. I have seen some text books use [x] to mean the GIV of x and I have seen another expression that broke off the top parts of the brackets so that it looked kinda like 2 L's facing each other.

In the GIV function, GIV(.9) = 0, GIV(1.1) = 1 and it is the guy that does what you are talking about.

If you are looking for an algorithm that will do the same thing as the GIV, you don't use the Mod operator. You cast it into integer form. If the computer uses truncation, you are done. If the processor uses rounding, then you want to subtract .5 from the number and then cast it as an integer. The rounding will then do the same thing as the GIV.

Answer 3

In most programming languages, you could say 10 div 3, (or just 10 / 3, since integer division gets you the result you want) but in mathematics, you want to use the floor operator on the result of the division.The floor operator takes any real value v and truncates down to the largest integer less than v. Similarly, the ceiling operator takes any value v and yields the smallest integer greater than v.

I don't know how to render these characters very well in html, but the left and right floor brackets look like square brackets with the top taken off. For example, ⌊ v ⌋ . The ceiling operator is similar, but with the bottom of the square bracket missing. ⌈ v ⌉ .

I've never seen square brackets by themselves used to mean the floor operator.

The mod operator (%) gives the remainder of the division, which is not what you are asking for.

Answer 4

Edit: My answer here is pretty retarded. I'm not sure what crack I was smoking because most of this is just b.s. Mod (%) just gives the remainder. If you want to actually get stupider then read my response, if not skip to the next one. She's all over this stuff.

-Start Retarded Answer-

For Computer Science the expression is Mod or % (at least when using C++), You won't find that in most normal math courses though. e.g. 10%3 = 3.

It isn't very useful outside of Comp. Sci. and that is the only context I've seen it in. It's called "Integer Divide" for fairly obvious reasons.

Edit: I am an idiot and forgot about the

[insert whatever expression you want between the brackets]

notation. That is the general way to express whatever you want in terms of lower bounding integers. e.g. [1/3] = [0.333...] = 0 and [4*(1/3)+(1/3)] = [1.66...] = 1

-End of Retarded Answer-

I'd give best answer to MathGirl if I were you.

Answer 5

In computer programming there is a way to do this but it depends on the specific computer language you are using. Look for functions like Mod in the help section to find the specific functions that will meet your needs.

Answer 6

mathgirl must be right,
it used to be absolute value with vertical lines,
no longer available