MA 3260 Lecture 14 - Multiplication Principle, Combinations, and
... If, for example, we have the set A = { 1, 2, 3 }, and we want to construct a subset S. There are three things to consider: (1) Do we want 1 ∈ S? (2) Do we want 2 ∈ S? (3) Do we want 3 ∈ S? The answer to each question is either Yes or No. In other words, each question has two choices. It may be natur ...
... If, for example, we have the set A = { 1, 2, 3 }, and we want to construct a subset S. There are three things to consider: (1) Do we want 1 ∈ S? (2) Do we want 2 ∈ S? (3) Do we want 3 ∈ S? The answer to each question is either Yes or No. In other words, each question has two choices. It may be natur ...
x 3 - Upm
... On the other hand, suppose that g: R → R is the function defined by g (x) = x4 – x for each real number x Let x1 = 0 and x2 =1.Then g(x1) = g(0) = (0)4 – 0 = 0 g(x2) = g(1) = (1)4 – (1) = 1 – 1 = 0 Hence g(x1) = g(x2) but x1 x2 (0 ≠ 1) – that is, g is not one to-one because there exist real number ...
... On the other hand, suppose that g: R → R is the function defined by g (x) = x4 – x for each real number x Let x1 = 0 and x2 =1.Then g(x1) = g(0) = (0)4 – 0 = 0 g(x2) = g(1) = (1)4 – (1) = 1 – 1 = 0 Hence g(x1) = g(x2) but x1 x2 (0 ≠ 1) – that is, g is not one to-one because there exist real number ...
A Proof of the Tietze Extension Theorem Using Urysohn`s Lemma
... A background in topology will undoubtedly be needed to get the most out of this paper, but in an attempt to make this paper accessible to all readers I will briefly define all pertinent terms. A topology on a set X is a family of subsets T such that the following properties hold: 1 Both the empty se ...
... A background in topology will undoubtedly be needed to get the most out of this paper, but in an attempt to make this paper accessible to all readers I will briefly define all pertinent terms. A topology on a set X is a family of subsets T such that the following properties hold: 1 Both the empty se ...
download_pptx
... We write |A| = |Z+| = ℵ0= aleph null A set that is not countable is called uncountable Proving the set is countable infinite involves (usually) constructing an explicit bijection with Z⁺ ...
... We write |A| = |Z+| = ℵ0= aleph null A set that is not countable is called uncountable Proving the set is countable infinite involves (usually) constructing an explicit bijection with Z⁺ ...
Functions
... Real Life Examples: A relation can be a relationship between sets of information. For example, consider the set of all of the people in your Algebra class and the set of their heights is a relation. The pairing of a person and his or her height is a relation. In relations and functions, the pairs o ...
... Real Life Examples: A relation can be a relationship between sets of information. For example, consider the set of all of the people in your Algebra class and the set of their heights is a relation. The pairing of a person and his or her height is a relation. In relations and functions, the pairs o ...
{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } A
... “set builder notation” is the most efficient and accurate way to describe these sets. A variable symbol is used to designate an unspecified member of the Universe: this slash is usually read “such that” the sentence gives the condition that ...
... “set builder notation” is the most efficient and accurate way to describe these sets. A variable symbol is used to designate an unspecified member of the Universe: this slash is usually read “such that” the sentence gives the condition that ...
The Learning Strands, Standards and Indicators Subject
... M.4.1.19. Distinguish whether the function is increasing or decreasing; M.4.1.20. Find the horizontal asymptote, range and y-intercept; M.4.1.21. Graph the exponential function; M.4.1.22. Express the concept of piecewise and step functions; M.4.1.23. Differentiate piecewise from a step function; M. ...
... M.4.1.19. Distinguish whether the function is increasing or decreasing; M.4.1.20. Find the horizontal asymptote, range and y-intercept; M.4.1.21. Graph the exponential function; M.4.1.22. Express the concept of piecewise and step functions; M.4.1.23. Differentiate piecewise from a step function; M. ...
m120cn3
... Addition of Whole Numbers The concept of whole number addition can be described (or defined) in terms of sets. If a set A contains a elements and a set B contains b elements, and AB=Ø, then a+b is the number of elements in AB. In the equation a+b=c, a and b are called the addends and c is called ...
... Addition of Whole Numbers The concept of whole number addition can be described (or defined) in terms of sets. If a set A contains a elements and a set B contains b elements, and AB=Ø, then a+b is the number of elements in AB. In the equation a+b=c, a and b are called the addends and c is called ...