We have showed the following sets are countable by constructing a
... Cantor diagonalization argument (1879) VERY powerful, important technique. Proof by contradiction. Sketch (details done on the board) - Assume countable - look at all numbers in the interval [0,1) - list them in ANY order - show that there is some number not listed ...
... Cantor diagonalization argument (1879) VERY powerful, important technique. Proof by contradiction. Sketch (details done on the board) - Assume countable - look at all numbers in the interval [0,1) - list them in ANY order - show that there is some number not listed ...
Full text
... The indices have been compiled using WORDPERFECT. Should you wish to order a copy of the indices for another wordprocessor or for a non-compatible IBM machine, please explain your situation to Dr. Cook when you place your order and he will try to accommodate you. DO NOT SEND PAYMENT WITH YOUR ORDER. ...
... The indices have been compiled using WORDPERFECT. Should you wish to order a copy of the indices for another wordprocessor or for a non-compatible IBM machine, please explain your situation to Dr. Cook when you place your order and he will try to accommodate you. DO NOT SEND PAYMENT WITH YOUR ORDER. ...
Algebra 2 compostion of functions
... pretty straight forward. The rules for the domain of functions would apply to these combinations of functions as well. The domain of the sum, difference or product would be the numbers x in the domains of both f and g. For the quotient, you would also need to exclude any numbers x that would make th ...
... pretty straight forward. The rules for the domain of functions would apply to these combinations of functions as well. The domain of the sum, difference or product would be the numbers x in the domains of both f and g. For the quotient, you would also need to exclude any numbers x that would make th ...
Test Unit 2 Answers - hhs
... h(t ) 5t 2 15t 90 gives the height of the golf ball above the water, where h(t) is the height in metres and t is the time in seconds. When will the ball hit the water? You must show an algebraic solution using what we have learned in this unit. [4] APP ...
... h(t ) 5t 2 15t 90 gives the height of the golf ball above the water, where h(t) is the height in metres and t is the time in seconds. When will the ball hit the water? You must show an algebraic solution using what we have learned in this unit. [4] APP ...
WEEK 1: CARDINAL NUMBERS 1. Finite sets 1.1. For a finite set A
... 1.1. For a finite set A, we will denote by #A the number of elements of A. 1.2. If A, B are two finite sets then #(A × B) = #A#̇B. 1.3. P (A), the power set of A, has 2#A elements. To see this, assume A = {1, 2, .., n}. Attach to each subset S ⊂ A the binary string y = y1 y2 ...yn where yi = 1 if i ...
... 1.1. For a finite set A, we will denote by #A the number of elements of A. 1.2. If A, B are two finite sets then #(A × B) = #A#̇B. 1.3. P (A), the power set of A, has 2#A elements. To see this, assume A = {1, 2, .., n}. Attach to each subset S ⊂ A the binary string y = y1 y2 ...yn where yi = 1 if i ...
here
... and so by the New Conjecture a = 1/2 or a = 1. But a = ℜ(s) and ℜ(s) < 1. Hence ℜ(s) = 1/2. Thus the New Conjecture implies the RH. Conversely, suppose the RH is true. Assume a and b satisfy condition (5). In particular, both series in (5) converge, and so their nth terms tend to 0 as n → ∞. It fol ...
... and so by the New Conjecture a = 1/2 or a = 1. But a = ℜ(s) and ℜ(s) < 1. Hence ℜ(s) = 1/2. Thus the New Conjecture implies the RH. Conversely, suppose the RH is true. Assume a and b satisfy condition (5). In particular, both series in (5) converge, and so their nth terms tend to 0 as n → ∞. It fol ...
1 Event spaces and probability measures
... 1.5 Borel sets of the two-dimensional Euclidean space. The Borel sigma-algebra B(R2 ) is defined as the smallest sigma-algebra on R2 which contains all open sets in R2 . Denote by π(R2 ) = {(−∞, x] × (−∞, y] : x ∈ R, y ∈ R}. the collection of closed lower rectangles in R2 . Prove that the collection ...
... 1.5 Borel sets of the two-dimensional Euclidean space. The Borel sigma-algebra B(R2 ) is defined as the smallest sigma-algebra on R2 which contains all open sets in R2 . Denote by π(R2 ) = {(−∞, x] × (−∞, y] : x ∈ R, y ∈ R}. the collection of closed lower rectangles in R2 . Prove that the collection ...
Math 2300: Calculus II Geometric series Goal: Derive the formula for
... (a) (i). Draw the square after three steps. What is the area of the shaded region? Write this as both an expanded sum, and as a single fraction. ...
... (a) (i). Draw the square after three steps. What is the area of the shaded region? Write this as both an expanded sum, and as a single fraction. ...
( )n ( )n Generation X and Y
... 5. Solve two equations for two unknowns (you now have c and d). 8. Apply The Root Theorem to problem 4 to show yourself that it works. Did it work? If so, it always works. (Do problem 5 if you must do something twice to consider it proved). Maybe The Root Theorem should have been called the: “Now I ...
... 5. Solve two equations for two unknowns (you now have c and d). 8. Apply The Root Theorem to problem 4 to show yourself that it works. Did it work? If so, it always works. (Do problem 5 if you must do something twice to consider it proved). Maybe The Root Theorem should have been called the: “Now I ...
Calculus 8.1
... If the second term of a geometric sequence is 6 and the fifth term is -48, find an explicit rule for the nth term. ...
... If the second term of a geometric sequence is 6 and the fifth term is -48, find an explicit rule for the nth term. ...
Define Function, Domain, and Range Identify Functions
... the same …rst coordinates and di¤erent second coordinates. > The domain of a relation is the set of all …rst coordinates of the ordered pairs. > The range of a relation is the set of all second coordinates of the ordered pairs. Example 1: (Finding the domain and range) Find the domain and range of t ...
... the same …rst coordinates and di¤erent second coordinates. > The domain of a relation is the set of all …rst coordinates of the ordered pairs. > The range of a relation is the set of all second coordinates of the ordered pairs. Example 1: (Finding the domain and range) Find the domain and range of t ...
