The Heart of Mathematics: An Invitation to Effective Thinking
4th Edition
ISBN: 9781118156599
Author: Edward B. Burger, Michael Starbird
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 3.2, Problem 22MS
A natural prune. Describe a collection of numbers you could remove from the set of natural numbers so that the set of remaining numbers contains fewer numbers than the set of all natural numbers. (Bonus: How many times did the word nwnbers appear in the previous sentence?)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Determine whether each function is an injection and determine whether each is a surjection.The notation Z_(n) refers to the set {0,1,2,...,n-1}. For example, Z_(4)={0,1,2,3}. f: Z_(6) -> Z_(6) defined by f(x)=x^(2)+4(mod6). g: Z_(5) -> Z_(5) defined by g(x)=x^(2)-11(mod5). h: Z*Z -> Z defined by h(x,y)=x+2y. j: R-{3} -> R defined by j(x)=(4x)/(x-3).
Determine whether each function is an injection and determine whether each is a surjection.
Let A
=
{a, b, c, d}, B = {a,b,c}, and C = {s, t, u,v}. Draw an arrow diagram of a function
for each of the following descriptions. If no such function exists, briefly explain why.
(a) A function f : AC whose range is the set C.
(b) A function g: BC whose range is the set C.
(c) A function g: BC that is injective.
(d) A function j : A → C that is not bijective.
Chapter 3 Solutions
The Heart of Mathematics: An Invitation to Effective Thinking
Ch. 3.1 - Still the one. What is a one-to-one...Ch. 3.1 - Prob. 2MSCh. 3.1 - Numerical nephwe. At a family gathering, your...Ch. 3.1 - Pile of packs. You walk into class late and notice...Ch. 3.1 - Bunch of balls. Your first job every morning at...Ch. 3.1 - The same, but unsure how much (H). We have used a...Ch. 3.1 - Taking stock (S). It turns out that there is a...Ch. 3.1 - Prob. 8MSCh. 3.1 - Heres looking @ ®. The following collections...Ch. 3.1 - Enough underwear. When Deb packs for a trip, she...
Ch. 3.1 - 791ZWV. Suppose a stranger tells you that the...Ch. 3.1 - 2452345. Suppose a stranger tells you that her...Ch. 3.1 - Social security (H). Is there a one-to-one...Ch. 3.1 - Testing one two three. A professor wishes to...Ch. 3.1 - Laundry day (ExH). Suppose you are given a bag of...Ch. 3.1 - Hair counts. Do there exist two nonbald people on...Ch. 3.1 - Social number (S). Social Security numbers contain...Ch. 3.1 - Prob. 18MSCh. 3.1 - Dining hall blues. One day in Ralph P. Uke Dining...Ch. 3.1 - Dorm life(H). Every student at a certain college...Ch. 3.1 - Pigeonhole principle. Recall the Pigeonhole...Ch. 3.1 - Mother and child. Every child has one and only one...Ch. 3.1 - Coast to coast. Jessica is working part-time from...Ch. 3.1 - An interesting correspondence. Suppose you invest...Ch. 3.1 - Chicken Little. With increased attention to eating...Ch. 3.1 - Table for four. The table below shows a one-to-one...Ch. 3.1 - Square table. The table below shows a one-to-one...Ch. 3.2 - Au natural. Describe the set of natural numbers.Ch. 3.2 - Prob. 2MSCh. 3.2 - Set setup. We can denote the natural numbers...Ch. 3.2 - Little or large. Which of the sets in Mindscape 3...Ch. 3.2 - A word you can count on. Define the cardinality of...Ch. 3.2 - Prob. 6MSCh. 3.2 - Naturally even. Let E stand for the set of all...Ch. 3.2 - Fives take over. Let EIF be the set of all natural...Ch. 3.2 - Six times as much (EH). If we let N stand for the...Ch. 3.2 - Any times as much. If we let N stand for the set...Ch. 3.2 - Missing 3 (H). Let TIM be the set of all natural...Ch. 3.2 - One weird set. Let OWS (you figure it out) be the...Ch. 3.2 - Squaring off. Let S stand for the set of all...Ch. 3.2 - Counting Cubes (formerly Crows). Let C stand for...Ch. 3.2 - Reciprocals. Suppose R is the set defined by R={...Ch. 3.2 - Hotel Cardinality (formerly California) (H). It is...Ch. 3.2 - Hotel Cardinality continued. Given the scenario in...Ch. 3.2 - More Hotel C (EH). Given the scenario in Mindscape...Ch. 3.2 - So much sand. Prove that there cannot be an...Ch. 3.2 - Prob. 20MSCh. 3.2 - Pruning sets. Suppose you have a set. If you...Ch. 3.2 - A natural prune. Describe a collection of numbers...Ch. 3.2 - Prune growth. Is it possible to remove things from...Ch. 3.2 - Same cardinality? Suppose we have two sets and we...Ch. 3.2 - Still the same? (S). Suppose we have two sets, and...Ch. 3.2 - Modest rationals (H). Devise and then describe a...Ch. 3.2 - A window of rationals. Using your answer to...Ch. 3.2 - Bowling ball barrel. Suppose you have infinitely...Ch. 3.2 - Not a total loss. Take the set of natural numbers...Ch. 3.2 - Prob. 30MSCh. 3.2 - Piles of peanuts (ExH). You have infinitely many...Ch. 3.2 - The big city (S). Not-Finite City (also known as...Ch. 3.2 - Dont lose your marbles. Suppose you have...Ch. 3.2 - Make a guess. Guess an infinite set that does not...Ch. 3.2 - Coloring. Consider the infinite collection of...Ch. 3.2 - Ping-Pong balls on parade (H). This Mindscape is...Ch. 3.2 - Primes. Show that the set of all prime numbers has...Ch. 3.2 - A grand union. Suppose you have two sets, and each...Ch. 3.2 - Unnoticeable pruning. Suppose you have any...Ch. 3.2 - Pink ping pong possibilities. You have a box...Ch. 3.2 - Plot the dots (H). The table below gives a...Ch. 3.2 - 1 to 1 or not 1 to 1? Does the table below give a...Ch. 3.2 - Roommates. Your school has 4000 students who want...Ch. 3.3 - Shake em up. What did Georg Cantor do that shook...Ch. 3.3 - Detecting digits. Heres a list of three numbers...Ch. 3.3 - Delving into digits. Consider the real number...Ch. 3.3 - Undercover friend (ExH). Your friend gives you a...Ch. 3.3 - Underhanded friend. Now you friend shows, you a...Ch. 3.3 - Dodgeball. Revisit the game of Dodgeball from...Ch. 3.3 - Dont dodge the connection (S). Explain the...Ch. 3.3 - Cantor with 3s and 7s. Rework Cantors proof from...Ch. 3.3 - Cantor with 4s and 8s. Rework Cantors proof from...Ch. 3.3 - Think positive. Prove that the cardinality of the...Ch. 3.3 - Diagonalization. Cantors proof is often referred...Ch. 3.3 - Digging through diagonals. First, consider the...Ch. 3.3 - Coloring revisited (ExH). In Mindscape 35 of the...Ch. 3.3 - Prob. 14MSCh. 3.3 - The first digit (H). Suppose that, in constructing...Ch. 3.3 - Ones and twos (H). Show that the set of all real...Ch. 3.3 - Pairs (S). In Cantors argument, is it possible to...Ch. 3.3 - Three missing. Given a list of real numbers, as in...Ch. 3.3 - Prob. 19MSCh. 3.3 - Prob. 20MSCh. 3.3 - Nines. Would Cantors argument work if we used 2...Ch. 3.3 - Missing irrational. Could you modify the...Ch. 3.3 - Logging cardinality. The function graphed here is...Ch. 3.3 - U-graph it. Using a graphic or on-line calculator,...Ch. 3.3 - Is a square a one-to-one correspondence? (H)...Ch. 3.3 - Is a cube a one-to-one correspondence? Sketch a...Ch. 3.3 - Find the digit. Your friend is thinking of a real...Ch. 3.4 - Prob. 1MSCh. 3.4 - Power play. Define the power set of a given set.Ch. 3.4 - Prob. 3MSCh. 3.4 - Prob. 4MSCh. 3.4 - Solar power. What is the cardinality of the power...Ch. 3.4 - All in the family (ExH). A family of four tries to...Ch. 3.4 - Making an agenda (H). There are eight members on...Ch. 3.4 - The power of sets (S). Let S={ !,@,#,$,%, }. Below...Ch. 3.4 - Prob. 9MSCh. 3.4 - Identifying the power. Let S be the set given by...Ch. 3.4 - Prob. 11MSCh. 3.4 - Another two. Suppose S is the set defined by S={...Ch. 3.4 - Prob. 13MSCh. 3.4 - Finite Cantor (H). Suppose that S is the set...Ch. 3.4 - One real big set. Describe (in words) a set whose...Ch. 3.4 - Prob. 16MSCh. 3.4 - The Ultra Grand Hotel (S). Could there be an...Ch. 3.4 - Prob. 18MSCh. 3.4 - Prob. 19MSCh. 3.4 - The number name paradox. Let S be the set of all...Ch. 3.4 - Adding another. Suppose that you have any infinite...Ch. 3.4 - Ones and twos. Describe a one-to-one...Ch. 3.4 - Enjoying the exponential function. Consider the...Ch. 3.4 - Prob. 28MSCh. 3.4 - Power play. Simplify the following expressions:...Ch. 3.4 - Powerful products. For each funciton given below,...Ch. 3.4 - Generalizing equality. Throughout this chapter we...Ch. 3.5 - Lining up. Can you draw a line segment that has...Ch. 3.5 - Reading between the lines. Use the figure below to...Ch. 3.5 - De line and Descartes. Put line segments L and M...Ch. 3.5 - Red line rendezvous (H). Given the equation for...Ch. 3.5 - Rendezvous two. Given the equation for the red...Ch. 3.5 - A circle is a cirde (H). Prove that a small circle...Ch. 3.5 - A circle is a square. Prove that a small circle...Ch. 3.5 - A circle is a triangle. Prove that a small circle...Ch. 3.5 - Stereo connections (ExH). Given the stereogiaphic...Ch. 3.5 - More stereo connections. Given the stereographic...Ch. 3.5 - Perfect shuffle problems (H). Suppose we used our...Ch. 3.5 - More perfect shuffle problems. Suppose we used our...Ch. 3.5 - Gouping digits. Given the grouping of digits...Ch. 3.5 - Where it came from. Given the grouping of digits...Ch. 3.5 - Group fix (S). Consider the point on the line from...Ch. 3.5 - Is there more to a cube? Prove that the...Ch. 3.5 - T and L (H). Prove that the cardinalities of...Ch. 3.5 - Infinitely long is long. Must it be the case that...Ch. 3.5 - Plugging up the north pole (ExH). What would...Ch. 3.5 - 3D stereo (S). Let S be the set of points on the...Ch. 3.5 - Stereo images. Given your answer to the preceding...Ch. 3.5 - Ground shuffle. Carefully verify that the pairing...Ch. 3.5 - Giving the rolled-up interval a tan. The graph...Ch. 3.5 - Back and forth. The function y=5x2 gives a...Ch. 3.5 - Forth and back. The function y=3x+1 gives a...Ch. 3.5 - Lining up (H). Find a function that gives a...Ch. 3.5 - Queuing up. Find a function that gives a...
Additional Math Textbook Solutions
Find more solutions based on key concepts
CHECK POINT I Let p and q represent the following statements: p : 3 + 5 = 8 q : 2 × 7 = 20. Determine the truth...
Thinking Mathematically (6th Edition)
2. Source of Data In conducting a statistical study, why is it important to consider the source of the data?
Elementary Statistics
Identifying Type I and Type II Errors In Exercises 31–36, describe type I and type II errors for a hypothesis t...
Elementary Statistics: Picturing the World (7th Edition)
76. Dew Point and Altitude The dew point decreases as altitude increases. If the dew point on the ground is 80°...
College Algebra with Modeling & Visualization (5th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Let f:R->R be defined by f(x)=x^(3)+5.(a) Determine if f is injective. why?(b) Determine if f is surjective. why?(c) Based upon (a) and (b), is f bijective? why?arrow_forwardLet f:R->R be defined by f(x)=x^(3)+5.(a) Determine if f is injective.(b) Determine if f is surjective. (c) Based upon (a) and (b), is f bijective?arrow_forwardPlease as many detarrow_forward
- 8–23. Sketching vector fields Sketch the following vector fieldsarrow_forward25-30. Normal and tangential components For the vector field F and curve C, complete the following: a. Determine the points (if any) along the curve C at which the vector field F is tangent to C. b. Determine the points (if any) along the curve C at which the vector field F is normal to C. c. Sketch C and a few representative vectors of F on C. 25. F = (2½³, 0); c = {(x, y); y − x² = 1} 26. F = x (23 - 212) ; C = {(x, y); y = x² = 1}) , 2 27. F(x, y); C = {(x, y): x² + y² = 4} 28. F = (y, x); C = {(x, y): x² + y² = 1} 29. F = (x, y); C = 30. F = (y, x); C = {(x, y): x = 1} {(x, y): x² + y² = 1}arrow_forward٣/١ B msl kd 180 Ka, Sin (1) I sin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 G 5005 1000 s = 1000-950 Copper bosses 5kW Rotor input 5 0.05 : loo kw 6) 1 /0001 ined sove in peaper I need a detailed solution on paper please وه اذا ميريد شرح الكتب فقط ١٥٠ DC 7) rotor a ' (y+xlny + xe*)dx + (xsiny + xlnx + dy = 0. Q1// Find the solution of: ( 357arrow_forward
- ۳/۱ R₂ = X2 2) slots per pole per phase 3/31 B. 180 msl Kas Sin (I) 1sin() sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30): 0.866 4) Rotating 5) Synchronous speeds 120×50 looo G 1000-950 1000 Copper losses 5kw Rotor input 5 loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط look 7) rotor DC ined sove in peaper I need a detailed solution on paper please 0 64 Find the general solution of the following equations: QI//y(4)-16y= 0. Find the general solution of the following equations: Q2ll yll-4y/ +13y=esinx.arrow_forwardR₂ = X2 2) slots per pole per phase = 3/31 B-180 60 msl kd Kas Sin () 2 I sin (6) sin(30) Sin (30) اذا مريد شرح الكتب بس 0 بالفراغ 3 Cos (30) 0.866 4) Rotating ined sove in peaper 5) Synchronous speed s 120×50 6 s = 1000-950 1000 Copper losses 5kw Rotor input 5 0.05 6) 1 loo kw اذا ميريد شرح الكتب فقط Look 7) rotov DC I need a detailed solution on paper please 0 64 Solve the following equations: 0 Q1// Find the solution of: ( y • with y(0) = 1. dx x²+y²arrow_forwardR₂ = X2 2) slots per pole per phase = 3/3 1 B-180-60 msl Ka Sin (1) Isin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 s = 1000-950 1000 Copper losses 5kw Rotor input 5 6) 1 0.05 G 50105 loo kw اذا ميريد شرح الكتب فقط look 7) rotov DC ined sove in peaper I need a detailed solution on paper please 064 2- A hot ball (D=15 cm ) is cooled by forced air T.-30°C, the rate of heat transfer from the ball is 460.86 W. Take for the air -0.025 Wim °C and Nu=144.89, find the ball surface temperature a) 300 °C 16 b) 327 °C c) 376 °C d) None か = 750 01arrow_forward
- Answer questions 8.3.3 and 8.3.4 respectively 8.3.4 .WP An article in Medicine and Science in Sports and Exercise [“Electrostimulation Training Effects on the Physical Performance of Ice Hockey Players” (2005, Vol. 37, pp. 455–460)] considered the use of electromyostimulation (EMS) as a method to train healthy skeletal muscle. EMS sessions consisted of 30 contractions (4-second duration, 85 Hz) and were carried out three times per week for 3 weeks on 17 ice hockey players. The 10-meter skating performance test showed a standard deviation of 0.09 seconds. Construct a 95% confidence interval of the standard deviation of the skating performance test.arrow_forward8.6.7 Consider the tire-testing data in Exercise 8.2.3. Compute a 95% tolerance interval on the life of the tires that has confidence level 95%. Compare the length of the tolerance interval with the length of the 95% CI on the population mean. Which interval is shorter? Discuss the difference in interpretation of these two intervals.arrow_forward8.6.2 Consider the natural frequency of beams described in Exercise 8.2.8. Compute a 90% prediction interval on the diameter of the natural frequency of the next beam of this type that will be tested. Compare the length of the prediction interval with the length of the 90% CI on the population mean. 8.6.3 Consider the television tube brightness test described in Exercise 8.2.7. Compute a 99% prediction interval on the brightness of the next tube tested. Compare the length of the prediction interval with the length of the 99% CI on the population mean.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Elementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice University
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Elementary Algebra
Algebra
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:OpenStax - Rice University
Finite State Machine (Finite Automata); Author: Neso Academy;https://www.youtube.com/watch?v=Qa6csfkK7_I;License: Standard YouTube License, CC-BY
Finite State Machine (Prerequisites); Author: Neso Academy;https://www.youtube.com/watch?v=TpIBUeyOuv8;License: Standard YouTube License, CC-BY