count

In mathematics, the essence of counting a set and finding a result n, is that it establishes a one-to-one correspondence (or bijection) of the set with the set of numbers {1, 2, ..., n}. A fundamental fact, which can be proved by mathematical induction, is that no bijection can exist between {1, 2, ..., n} and {1, 2, ..., m} unless n = m; this fact (together with the fact that two bijections can be composed to give another bijection) ensures that counting the same set in different ways can never result in different numbers (unless an error is made). This is the fundamental mathematical theorem that gives counting its purpose; however you count a (finite) set, the answer is the same. In a broader context, the theorem is an example of a theorem in the mathematical field of (finite) combinatorics—hence (finite) combinatorics is sometimes referred to as "the mathematics of counting."

count (n.1), title of nobility in some continental nations, corresponding to English earl, c. 1300, from Anglo-French counte "count, earl" (Old French conte), from Latin comitem (nominative comes) "companion, attendant," the Roman term for a provincial governor, from com "with" + stem of ire "to go" (from PIE root *ei- "to go"). The term was used in Anglo-French to render Old English eorl, but the word was never truly naturalized and mainly was used with reference to foreign titles.

count (n.2), early 14c., "a counting, a calculation," also "an account of money or property;" late 15c., "the total number, the total counted," from Anglo-French counte, Old French conte "a count, a reckoning, calculations," from conter "to count, add up," from Latin computare "to count, sum up, reckon together" (see compute).

Meaning "estimation, esteem, consideration" is from late 15c. In law, "each charge in an indictment," from 1580s. In boxing, "the counting by the referee of the 10 seconds allowed a fallen fighter to get up again," by 1902. In baseball and softball, "the number of strikes and balls thrown to a batter in a turn at the plate," by 1909.

六级/考研单词: mathematics, essence, compose, finite, noble, continent, correspond, nominate, companion, province, stem, render, reckon, compute, esteem, indict, boxing, referee, batter