Index numbers vs. Quantity in a group

[1plus1is10]

"Quantity in a group"
If you have 6 apples and you subtract 4, then you have 2 apples left "in the group".

"Quantity in an Indexed group"
I'm a computer programmer - I manipulate arrays of data (a.k.a. matrix)
In a math formula format: x₁, x₂, x₃... x_n
(as a side note - in a computer format: x[0], x[1], x[2]... x[n-1])
If I want the "quantity" from 6 to 4, then I always have to add 1 (6-4=2, 2+1=3 quantity)
Quantity of 3: x₄, x₅, x₆

Surprisingly, I was never taught this in grade school or high school.
Not to mention I always thought it had to do with the fact that a computer's array starts with index 0: x[0]
(It doesn't, although that fact adds confusion when turning math formulas into code)

My question is: Does this "add 1" scenario have a mathematical name?
(I've been trying to Google about it to add a note/comment to my code to explain "+1" without sounding stupid)

Thanks

 

[Mark44]

"Quantity in a group"
If you have 6 apples and you subtract 4, then you have 2 apples left "in the group".

"Quantity in an Indexed group"
I'm a computer programmer - I manipulate arrays of data (a.k.a. matrix)
In a math formula format: x₁, x₂, x₃... x_n
(as a side note - in a computer format: x[0], x[1], x[2]... x[n-1])
If I want the "quantity" from 6 to 4, then I always have to add 1 (6-4=2, 2+1=3 quantity)
Quantity of 3: x₄, x₅, x₆

Surprisingly, I was never taught this in grade school or high school.
Not to mention I always thought it had to do with the fact that a computer's array starts with index 0: x[0]
(It doesn't, although that fact adds confusion when turning math formulas into code)

My question is: Does this "add 1" scenario have a mathematical name?
(I've been trying to Google about it to add a note/comment to my code to explain "+1" without sounding stupid)

Thanks

The closest I can come up with for a name is when you miscount -- a "fence-post" error. The number of elements in the range $x_m$ through $x_n$, inclusive, with $n \ge m$, is n - m + 1. For example, the number of elements in the range $x_3$ through $x_7$, again inclusive, is 7 - 3 + 1 = 5. They are $x_3, x_4, x_5, x_6, x_7$. This type of counting typically isn't taught in grade school or high school (that I am aware of), but it is taught in basic computer science classes, or possibly in probability and statistics courses.

 

[1plus1is10]

"fence-post" error

Wow, perfect. I learned something new today.

Wikipedia has it described under: Off-by-one error (OBOE)
https://en.wikipedia.org/wiki/Off-by-one_error
Thanks Mark

 

[1plus1is10]

Wow again...
This also explains the age-old problem/confusion with year/century (e.g. the 1900's is the 20th century).
Cool man.