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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

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

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
ChapterCSR: Contents Of Student Resources
Section: Chapter Questions
Problem 15.2P
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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
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