[Math] Intervals: examples of closed intervals

... In many parts of mathematics ( recall \( \sum^{max}_{x=1} f(x) \) ).

Closed interval denoted as [begin, end] (inclusive).

Closed interval in Wolfram Mathematica:

In[4]:= Sum[x,{x,1,10}]
Out[4]= 55

...

In[2]:= Table[x,{x,1,10}]
Out[2]= {1,2,3,4,5,6,7,8,9,10}

(BTW, vectors often started at index 1, like in Wolfram Mathematica and also FORTRAN.)

The notation ":" denotes a subarray. Thus, A[i : j] indicates the subarray of A
consisting of the elements A[i], A[i + 1], ..., A[j]. We also use this notation
to indicate the bounds of an array, as we did earlier when discussing the array
A[1 : n].
...
7 If you’re used to programming in Python, bear in mind that in this book,
the subarray A[i : j]
includes the element A[j]. In Python, the last element of A[i : j] is A[j - 1].
Python allows negative
indices, which count from the back end of the list.
This book does not use negative array indices.

GNU coreutils, README file:

For any copyright year range specified as YYYY-ZZZZ in this package
note that the range specifies every single year in that closed interval.

UNIX shell and regexps: [a-z] is closed interval.

If your rating in Uber is 4.8, it's in fact lies in [4.75, 4.85], due to rounding:

% python3
>>> "%1.1f" % 4.75
'4.8'
>>> "%1.1f" % 4.85
'4.8'
>>> "%1.1f" % 4.849999999999
'4.8'
>>> "%1.1f" % 4.850000000001
'4.9'

Also closed interval:

random.randint(a, b)

Return a random integer N such that a <= N <= b. Alias for randrange(a, b+1).

( https://docs.python.org/3/library/random.html )

From suckless st. BETWEEN: this is closed interval.

#define BETWEEN(x, a, b)    ((a) <= (x) && (x) <= (b))
...

#define ISCONTROLC0(c)      (BETWEEN(c, 0, 0x1f) || (c) == 0x7f)
#define ISCONTROLC1(c)      (BETWEEN(c, 0x80, 0x9f))
...
int
selected(int x, int y)
{
    if (sel.mode == SEL_EMPTY || sel.ob.x == -1 ||
            sel.alt != IS_SET(MODE_ALTSCREEN))
        return 0;

    if (sel.type == SEL_RECTANGULAR)
        return BETWEEN(y, sel.nb.y, sel.ne.y)
            && BETWEEN(x, sel.nb.x, sel.ne.x);

    return BETWEEN(y, sel.nb.y, sel.ne.y)
        && (y != sel.nb.y || x >= sel.nb.x)
        && (y != sel.ne.y || x <= sel.ne.x);
}

Colloquial speech: "buy 10-15 eggs", "I drink 2-4 shots at evening"

(the post first published at 20251118, updated 20251119.)

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