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dplyr is an R package whose set of functions are designed to enable dataframe (a spreadsheet-like data structure) manipulation in an intuitive, user-friendly way. It is one of the core packages of the popular tidyverse set of packages in the R programming language . [ 1 ]
Tally marks, also called hash marks, are a form of numeral used for counting. They can be thought of as a unary numeral system. They are most useful in counting or tallying ongoing results, such as the score in a game or sport, as no intermediate results need to be erased or discarded. However, because of the length of large numbers, tallies ...
The Only Three Questions that Count: Investing by Knowing What Others Don't is a book on investment advice by Ken Fisher. It was released in December 2006 and spent three months on The New York Times list of "Hardcover business bestsellers" . [1] It was also a Wall Street Journal and a BusinessWeek best seller. [2]
The MIT Blackjack Team was a group of students and ex-students. The students were from Massachusetts Institute of Technology, Harvard University, and other leading colleges; they used card counting techniques and more sophisticated strategies to beat casinos at blackjack worldwide. The team and its successors operated successfully from 1979 ...
The consequences of the theorem include: the order of a group G is a power of a prime p if and only if ord(a) is some power of p for every a in G. [2] If a has infinite order, then all non-zero powers of a have infinite order as well. If a has finite order, we have the following formula for the order of the powers of a: ord(a k) = ord(a) / gcd ...
Where double counting involves counting one set in two ways, bijective proofs involve counting two sets in one way, by showing that their elements correspond one-for-one. The inclusion–exclusion principle , a formula for the size of a union of sets that may, together with another formula for the same union, be used as part of a double ...
Cauchy's theorem is generalized by Sylow's first theorem, which implies that if p n is the maximal power of p dividing the order of G, then G has a subgroup of order p n (and using the fact that a p-group is solvable, one can show that G has subgroups of order p r for any r less than or equal to n).
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