# Inclusive and exclusive classes.

1. Sep 16, 2009

### dE_logics

Inclusive -
This basically means that suppose in the interval -
x – y
The range starts from x and ends after y, that is including all possible values of y.
So if we have a class interval 5 – 10 which is inclusive, then it will include 10.9999999999999999999999999999999999....
When constructing classes off this, since all values in the range of value 10 are included in 5 – 10, the next class should start from 11 to include new values. If it starts form 10, it will be invalid since it will include repetition of data.
0 - 5
6 – 11
12 – 17
etc...

Exclusive -
For an interval -
x – y
if this interval is exclusive, it will mean that values in this class starts from x and ends before y, that is it contains all values in the range of the constant y – 1.
So subtraction is exclusive.
For example class 5 – 10 will include values till 9.999999999999999999999999999999999
When constructing classes using exclusive intervals, we need to do it such that all possible values of variables come into it.
So construction of exclusive classes will be like -
0 - 5
5 – 10
10 – 15
The reason for including 10 in the next class is cause first class does not contain values in the domain 10.

2. Sep 17, 2009

### dE_logics

Ok, the definition of inclusive was wrong...this is the right one -

Inclusive -
This basically means that suppose in the interval -
x – y
The range starts from x and ends at y, that is including all possible values of y-1.
So if we have a class interval 5 – 10 which is inclusive, then it will include 10 or end at 10, 10.00000000000000000000000000...1 wont be included in this class interval but 9.999999999999999999999999999999999 – 10 will be.
Using this strategy, if we want to include all possible values of a variable while making groups, we have to do this -
0 – 5
5.000000000000000000000000000....1 – 9.0000000000000000000000....1
9.0000000000000000...2 – 14.0000000000000000000000000000000....2
and so on.
This is the consequence of the fact that 0 – 5 will contain all values TILL 5, so to ensure that there's no data loss (or repetition) in between the classes, the next class should start with “5.000000000000000000000000000....1”...since this is really not defined, we use -
0 - 5
6 – 11
12 – 17
etc...
In this case, the values between 5 and 6 have been omitted...i.e if we have a value greater than 5 and less than 6, we don't have any place to place them.
Such classes, although will not be continuous, is at least writable, so by formal define such classes as above are called 'inclusive' cause they are assumed to have included the value of the class limit.

3. Sep 18, 2009

### tiny-tim

Hi dE_logics!

I don't really understand your question.

"inclusive interval", more usually called "closed interval", written [x,y], means all numbers ≥ x and ≤ y

"exclusive interval", more usually called "open interval", written (x,y), means all numbers > x and < y

Is that what you meant?

4. Sep 18, 2009

### Tac-Tics

Like tiny-tim said, use interval notation.

If you want to divide a range of numbers into non-overlapping intervals, the easiest way to do it is to use half-open intervals.

[a, b) is the set of all numbers x where a <= x < b. It's called half-open (or half closed or "clopen") because it's inclusive on one side and exclusive on the other. If you have two such half-open intervals [a, b) and [b, c), they push up right next to each other with no overlap. If x is between a and b, it is in the first class. If x is between b and c, it's in the second class. If x = b, then it's also in the second class, due to the fact b is only inclusive in [b, c).

This trick is extremely useful in programming. For example, in Python, the function range(n) returns the list of numbers [0, 1, ..., n-1]. This is the interval [0, n) for integers. And the slice notation, list[a:b], returns the sublist containing the elements of list whose indexes are in [a, b).

5. Sep 21, 2009

### dE_logics

Can you provide some reference?...in terms of statistics...cause I read everywhere that all numbers >= x and < y

6. Sep 21, 2009

### tiny-tim

(have a ≥ )

That looks like the half-open interval, [x,y), that Tac-Tics mentioned.

(But I think you can use anything, so long as they all fit together)

7. Sep 22, 2009

### dE_logics

Ok then, I'm quiet sure about what I concluded...thanks!