Counting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every element of the set, in some order, while marking (or displacing) those elements to avoid visiting the same element more than once, until no unmarked elements are left; if the counter was set to one after the first object, the value after visiting the final object gives the desired number of elements. The related term enumeration refers to uniquely identifying the elements of a finite (combinatorial) set or infinite set by assigning a number to each element.
There is archaeological evidence suggesting that humans have been counting for at least 50,000 years.[1] Counting was primarily used by ancient cultures to keep track of social and economic data such as the number of group members, prey animals, property, or debts (that is, accountancy). Notched bones were also found in the Border Caves in South Africa, which may suggest that the concept of counting was known to humans as far back as 44,000 BCE.[2] The development of counting led to the development of mathematical notation, numeral systems, and writing.
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Verbal counting involves speaking sequential numbers aloud or mentally to track progress. Generally such counting is done with base 10 numbers: "1, 2, 3, 4", etc. Verbal counting is often used for objects that are currently present rather than for counting things over time, since following an interruption counting must resume from where it was left off, a number that has to be recorded or remembered.
Counting a small set of objects, especially over time, can be accomplished efficiently with tally marks: making a mark for each number and then counting all of the marks when done tallying. Tallying is base 1 counting.
Musical terminology also uses inclusive counting of 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.
Learning to count is an important educational/developmental milestone in most cultures of the world. Learning to count is a child's very first step into mathematics, and constitutes the most fundamental idea of that discipline. However, some cultures in Amazonia and the Australian Outback do not count,[6][7] and their languages do not have number words.
Many children at just 2 years of age have some skill in reciting the count list (that is, saying "one, two, three, ..."). They can also answer questions of ordinality for small numbers, for example, "What comes after three?". They can even be skilled at pointing to each object in a set and reciting the words one after another. This leads many parents and educators to the conclusion that the child knows how to use counting to determine the size of a set.[8] Research suggests that it takes about a year after learning these skills for a child to understand what they mean and why the procedures are performed.[9][10] In the meantime, children learn how to name cardinalities that they can subitize.
Many sets that arise in mathematics do not allow a bijection to be established with {1, 2, ..., n} for any natural number n; these are called infinite sets, while those sets for which such a bijection does exist (for some n) are called finite sets. Infinite sets cannot be counted in the usual sense; for one thing, the mathematical theorems which underlie this usual sense for finite sets are false for infinite sets. Furthermore, different definitions of the concepts in terms of which these theorems are stated, while equivalent for finite sets, are inequivalent in the context of infinite sets.
The notion of counting may be extended to them in the sense of establishing (the existence of) a bijection with some well-understood set. For instance, if a set can be brought into bijection with the set of all natural numbers, then it is called "countably infinite." This kind of counting differs in a fundamental way from counting of finite sets, in that adding new elements to a set does not necessarily increase its size, because the possibility of a bijection with the original set is not excluded. For instance, the set of all integers (including negative numbers) can be brought into bijection with the set of natural numbers, and even seemingly much larger sets like that of all finite sequences of rational numbers are still (only) countably infinite. Nevertheless, there are sets, such as the set of real numbers, that can be shown to be "too large" to admit a bijection with the natural numbers, and these sets are called "uncountable." Sets for which there exists a bijection between them are said to have the same cardinality, and in the most general sense counting a set can be taken to mean determining its cardinality. Beyond the cardinalities given by each of the natural numbers, there is an infinite hierarchy of infinite cardinalities, although only very few such cardinalities occur in ordinary mathematics (that is, outside set theory that explicitly studies possible cardinalities).
The domain of enumerative combinatorics deals with computing the number of elements of finite sets, without actually counting them; the latter usually being impossible because infinite families of finite sets are considered at once, such as the set of permutations of {1, 2, ..., n} for any natural number n.
The Crowd Counting Consortium (CCC), a joint project of Harvard Kennedy School and the University of Connecticut, collects publicly available data on political crowds reported in the United States, including marches, protests, strikes, demonstrations, riots, and other actions.
We only post records that we can confirm and verify through fact-checking. When you submit a record, be sure to provide a source that is publicly verifiable (e.g. a news report, a Facebook group, links to online photos with headcounts, etc) or describe the crowd-counting techniques used by onsite onlookers (e.g. sign-ins, counting through distributing flyers/handouts, counting from photos/videos, and/or other crowd density estimation techniques).
We collect publicly available data on political crowds reported in the United States, including marches, protests, demonstrations, riots, and other actions. We do not count crowds at meetings, teach-ins or academic workshops, panel discussions, fundraisers, or town halls.
New Crowd Counting Consortium analysis from Nonviolent Action Lab Program Director Jay Ulfelder sets the record straight on arrests numbers and claims of violence stemming from protests sparked by the war in Gaza.
To make it easier to find up-to-date information on pro-Palestine and pro-Israel protest activity in the United States since October 7, 2023, the Crowd Counting Consotium recently created a pair of interactive data dashboards separately covering the two.
On Tuesday, December 5th, 2023, experts from the Crowd Counting Consortium, a network of researchers tracking political demonstrations across the U.S., shared their most recent data on the multitude of pro-Israeli and pro-Palestinian protests held nationwide since October 7.
Since October 7, the Crowd Counting Consortium (CCC) has recorded nearly 2,300 U.S. protests, rallies, marches, caravans, demonstrations, vigils, banner drops, and direct actions in support of Palestine or Israel, with hundreds of thousands of total participants on different sides of this mass mobilization.
Over the past 10 days, the wave of U.S. street activism supporting Palestine has accelerated. Since October 7, 2023, when Palestinian militants launched attacks on Israel that killed more than 1,400 people, CCC has logged 420 pro-Palestine rallies, protests, demonstrations, and vigils in more than 180 different cities and towns across 46 states, the District of Columbia, Puerto Rico, and Guam.
After a year that saw historic levels of anti-LGBTQ+ protest activity, legislative action, and online jawboning, millions of people turned out in May and June 2023 for hundreds of LGBTQ+ pride celebrations across all 50 U.S. states and the District of Columbia.
On Saturday, May 20, 2023, more than 1,000 tenants, union members, community organizers, and politicians gathered at Cadman Plaza in the rain and then marched across the Brooklyn Bridge to call for lower rents in New York City and the passage of state legislation to protect tenants from eviction without good cause.
I need assistance with counting blanks in the due date column in my smartsheet. I used the formula =IF(ISABLANK({National Alliance Operation Inquiries Range 2}1),"BLANK", "NOT BLANK") but it seems not to work. Screenshots have been attached for your review.
Then you could use a cross-sheet COUNTIF formula to count how many of the cells say "BLANK", if that's what you're going for. If neither of these work for you, it would be very useful to see the screen captures you mentioned.
If it makes you feel any better... My initial thought for something like this is always an ISBLANK function. Even after all of the formulas written and time spent I still have to remind myself that "" is the same thing as blank and saves a few keystrokes (not to mention cuts out a set of those pesky parenthesis).
Thank you both! :-) It seems like the formula is counting more cells than are in that column. For example, I exported the spreadsheet to compare the blanks and the spreadsheet has 83 blank cells when the formula returned 93. I am trying to attach screenshots but it just keep saying loading......
Would you be able to explain a little further what you're looking to do, or what the scenario is? A helper column indicating when a cell is blank, but only if the row has other information, may be another way to go (then you can count that helper column instead of just blank cells).
@Genevieve P Thank you! Not to say your solution was wrong. Just that there were multiple ways of accomplishing it. I personally try to only add columns when necessary, but I have worked with other people that love adding in helper columns because the formulas themselves are generally a little less complex. 152ee80cbc