0.510152025303. 13. Coloring revisited (ExH). In Mindscape III.35 of the previous section we considered the following infinite collection of circles and all the different ways of coloring the circles with either red or blue markers. Show that the set of all possible circle colorings has a greater cardinality than the set of all natural numbers. ... O-0-0-0-00-0-0-0-0-0-0

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.1: Basic Assumptions
Problem 40WE
icon
Related questions
Question

coloring revisited. 

show that the set of all possible circle colorings has a greater cardinality than the set of all natural numbers

 

10. Think positive. Prove
is the same as the cardinality of the nega
You need to describe a one-to-one correspondence; howe"
remember that you cannot list the elements in a table.)
diagonalization is a reasonable
12. the infinite
this list of argument,
11. is often to as “Cantor
collection of in how these
name.
numbers are constructed (that is, describe the procedure for generati
this list of numbers). Then, using Cantor's diagonalization argumen
find a number not on the list. Justify your answer.
0.123456789101112131415161718...
0.2468101214161820222426283032. . .
0.369121518212427303336394245...
0.4812162024283236404448525660. .
0.510152025303540455055606570. . .
13. Coloring revisited (ExH). In Mindscape III.35 of the previous
section we considered the following infinite collection of circles and
all the different ways of coloring the circles with either red or blue
markers. Show that the set of all possible circle colorings has a greater
cardinality than the set of all natural numbers.
14. A penny for their thoughts. Suppose you had infinitely many people,
each one wearing a uniquely numbered button: 1, 2, 3, 4, 5, . . . (you
can use all the people in the Hotel Cardinality if you don't know
0-0-0-0-0-0-0-0-0-0-0-0-
nok)
enough people yourself). You also have lots of pennies (infinitely
many, so you're really rich; but don't try to carry them all around
Transcribed Image Text:10. Think positive. Prove is the same as the cardinality of the nega You need to describe a one-to-one correspondence; howe" remember that you cannot list the elements in a table.) diagonalization is a reasonable 12. the infinite this list of argument, 11. is often to as “Cantor collection of in how these name. numbers are constructed (that is, describe the procedure for generati this list of numbers). Then, using Cantor's diagonalization argumen find a number not on the list. Justify your answer. 0.123456789101112131415161718... 0.2468101214161820222426283032. . . 0.369121518212427303336394245... 0.4812162024283236404448525660. . 0.510152025303540455055606570. . . 13. Coloring revisited (ExH). In Mindscape III.35 of the previous section we considered the following infinite collection of circles and all the different ways of coloring the circles with either red or blue markers. Show that the set of all possible circle colorings has a greater cardinality than the set of all natural numbers. 14. A penny for their thoughts. Suppose you had infinitely many people, each one wearing a uniquely numbered button: 1, 2, 3, 4, 5, . . . (you can use all the people in the Hotel Cardinality if you don't know 0-0-0-0-0-0-0-0-0-0-0-0- nok) enough people yourself). You also have lots of pennies (infinitely many, so you're really rich; but don't try to carry them all around
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Recommended textbooks for you
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning