Editing Counting (section)

==Inclusive counting==
Inclusive/exclusive counting are two different methods of counting. For exclusive counting, unit intervals are counted at the end of each interval. For inclusive counting, unit intervals are counted beginning with the start of the first interval and ending with end of the last interval. This results in a count which is always greater by one when using inclusive counting, as compared to using exclusive counting, for the same set. Apparently, the introduction of the number zero to the number line resolved this difficulty; however, inclusive counting is still useful for some things. 

Refer also to the [[fencepost error]], which is a type of [[off-by-one error]]. 

Modern mathematical English language usage has introduced another difficulty, however. Because an exclusive counting is generally tacitly assumed, the term "inclusive" is generally used in reference to a set which is actually counted exclusively. For example; How many numbers are included in the set that ranges from 3 to 8, inclusive? The set is counted exclusively, once the range of the set has been made certain by the use of the word "inclusive". The answer is 6; that is 8-3+1, where the +1 range adjustment makes the adjusted exclusive count numerically equivalent to an inclusive count, even though the range of the inclusive count does not include the number eight unit interval. So, it's necessary to discern the difference in usage between the terms "inclusive counting" and "inclusive" or "inclusively", and one must recognize that it's not uncommon for the former term to be loosely used for the latter process. 

Inclusive counting is usually encountered when dealing with time in [[Roman calendar]]s and the [[Romance language]]s.<ref name="Evans">{{cite book |first=James |last=Evans |chapter-url=https://books.google.com/books?id=LVp_gkwyvC8C&pg=PA164 |title=The History and Practice of Ancient Astronomy |publisher=Oxford University Press |year=1998 |isbn=019987445X|chapter=4 |page=164}}</ref> In the [[ancient Roman calendar]], the ''nones'' (meaning "nine") is 8 days before the ''ides''; more generally, dates are specified as inclusively counted days up to the next named day.<ref name="Evans" /> 

In the [[Christian liturgical calendar]], [[Quinquagesima]] (meaning 50) is 49&nbsp;days before Easter Sunday. When counting "inclusively", the Sunday (the start day) will be ''day 1'' and therefore the following Sunday will be the ''eighth day''. For example, the French phrase for "[[fortnight]]" is ''quinzaine'' (15&nbsp;[days]), and similar words are present in Greek (δεκαπενθήμερο, ''dekapenthímero''), Spanish (''quincena'') and Portuguese (''quinzena''). 

In contrast, the English word "fortnight" itself derives from "a fourteen-night", as the archaic "[[wikt:sennight|sennight]]" does from "a seven-night"; the English words are not examples of inclusive counting.  In exclusive counting languages such as English, when counting eight days "from Sunday", Monday will be ''day 1'', Tuesday ''day 2'', and the following Monday will be the ''eighth day''.{{citation needed |date=April 2021 |reason=I am unaware of any firm basis for this assertion. It is highly culturally dependent.}} For many years it was [[History of taxation in the United Kingdom#Legal rule|a standard practice in English law]] for the phrase "from a date" to mean "beginning on the day after that date": this practice is now deprecated because of the high risk of misunderstanding.<ref>{{Cite web |title=Drafting bills for Parliament |url=https://www.gov.uk/government/publications/drafting-bills-for-parliament |website=gov.uk |date=18 June 2020 |publisher=Office of the Parliamentary Counsel}} See heading 8.</ref>

Similar counting is involved in [[East Asian age reckoning]], in which [[newborn]]s are considered to be 1 at birth.

Musical terminology also uses inclusive counting of [[interval (music)|intervals]] between notes of the standard scale: going up one note is a second interval, going up two notes is a third interval, etc., and going up seven notes is an ''[[octave]]''.