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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
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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