Lecture notes 3 -- Cardinality
... we denote the size of a set A by |A|. We can now use this definition of size to discuss not only sets containing numbers, but also sets containing arbitrary elements including colors, cities, and people. We can show that |;| = 0, and note that the empty set is in fact the only such set with size 0. ...
... we denote the size of a set A by |A|. We can now use this definition of size to discuss not only sets containing numbers, but also sets containing arbitrary elements including colors, cities, and people. We can show that |;| = 0, and note that the empty set is in fact the only such set with size 0. ...
Finding Absolute Value and Adding/Subtracting Real Numbers
... Keep the sign of the larger number Then you’ll be exact. ...
... Keep the sign of the larger number Then you’ll be exact. ...
Set-Builder Notation
... Roster Notation • Roster Notation means to explicitly list the elements of a set – When listing elements, we use set notation and place the elements between and left { and right } (called curly braces) – We use … (ellipses) to denote a set extending infinitely in the same pattern • The set of even ...
... Roster Notation • Roster Notation means to explicitly list the elements of a set – When listing elements, we use set notation and place the elements between and left { and right } (called curly braces) – We use … (ellipses) to denote a set extending infinitely in the same pattern • The set of even ...
Lecture 7: Sequences, Sums and Countability
... 0 bit-strings yet R is uncountable, there can be no onto function from computer programs to decimal numbers. In particular, most numbers do not correspond to any computer program so are ...
... 0 bit-strings yet R is uncountable, there can be no onto function from computer programs to decimal numbers. In particular, most numbers do not correspond to any computer program so are ...
File
... Suppose you are delivering mail in an office building. You leave the mailroom and enter the elevator next door. You go up four floors, down seven, and up nine to the executive offices on the top floor. Then, you go down six, up two, and down eight to the lobby on the first floor. What floor is the m ...
... Suppose you are delivering mail in an office building. You leave the mailroom and enter the elevator next door. You go up four floors, down seven, and up nine to the executive offices on the top floor. Then, you go down six, up two, and down eight to the lobby on the first floor. What floor is the m ...
Infinity
Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics.In mathematics, ""infinity"" is often treated as if it were a number (i.e., it counts or measures things: ""an infinite number of terms"") but it is not the same sort of number as natural or real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number; see 1/∞.Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.