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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.

          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.
        
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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.

Added by Allison W.

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Elementary and Intermediate Algebra
Elementary and Intermediate Algebra
Alan S. Tussy, R. David Gustafson 5th Edition
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13. Coloring revisited in Mindscape III.35 of the previous markers. Show that the set of all possible circle colorings has a greater cardinality than the set of all natural numbers.
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00:01 Hi, today we are solving the question in which we need to find a bijection between the set of all infinite sequences having 0s and 1 and the set of all binary numbers in the interval 0 or 1.
00:15 So we can do this by associating each infinite sequence with a unique binary number in interval 0 or 1 by associating.
00:46 And similarly, we need to find a bijection between the set of all number binary in the interval 0 or 1 and the set of all real number in the interval 0 or 1.
00:58 So we can do this by using the binary representation of real numbers as 0 .010101 corresponds to real number 0 .333 in base 10.
01:27 Finally we need to find a bijection between the set of all real number in the interval 0 or 1 and the continuum r.
01:36 So we can do this by using the function fx is equals to 2x minus 1 which maps to the interval 0 or 1 on the entire real line.
01:50 Combining these three bijection, combining these bijection, we have a bijection between the set t of all infinite sequence of 0 and 1 and the continuum r...
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