0.1 Numbers and Sets Real Numbers
... The _______________________of two sets A and B is the set of elements that are in either A or B. A ∪ B = { x | x ∈ A or x ∈ B}. The ____________________________of two sets A and B is the set of elements that are in both A and B. A ∩ B = { x | x ∈ A and x ∈ B}. ...
... The _______________________of two sets A and B is the set of elements that are in either A or B. A ∪ B = { x | x ∈ A or x ∈ B}. The ____________________________of two sets A and B is the set of elements that are in both A and B. A ∩ B = { x | x ∈ A and x ∈ B}. ...
Infinity and Beyond
... set and the natural numbers, N? The answer to this question is no, in light of the ternary representation of the Cantor set, C, and using Cantor’s Diagonalization Argument. What about the real numbers? Consider the subset of the real numbers on the interval ...
... set and the natural numbers, N? The answer to this question is no, in light of the ternary representation of the Cantor set, C, and using Cantor’s Diagonalization Argument. What about the real numbers? Consider the subset of the real numbers on the interval ...
Section 2.4 Countable Sets
... which means the cardinality of a denumerable set can not be greater than the cardinality of any infinite set. Hence, ℵ0 it is the smallest transfinite number. Note: The symbol " ∞ " , the reader is well aware of from calculus, does not meant to stand for an infinite set. The phrase x → ∞ simply refe ...
... which means the cardinality of a denumerable set can not be greater than the cardinality of any infinite set. Hence, ℵ0 it is the smallest transfinite number. Note: The symbol " ∞ " , the reader is well aware of from calculus, does not meant to stand for an infinite set. The phrase x → ∞ simply refe ...
Homework #3
... If there is a person p who knows everyone in the group, then there cannot also be a person r who knows nobody else. Either p and r know each other (and thus r knows someone), or they do not (and thus p does not know everyone). Thus R can contain either 0 or n – 1, but not both, so in no case can R h ...
... If there is a person p who knows everyone in the group, then there cannot also be a person r who knows nobody else. Either p and r know each other (and thus r knows someone), or they do not (and thus p does not know everyone). Thus R can contain either 0 or n – 1, but not both, so in no case can R h ...
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.