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 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 at once). Now you give each person a penny; then ask everyone to flip his or her penny at the same time. Then ask them to shout out in order what they flipped (H for heads and T for tails). So you might hear: HHTHHTTTHTTHTHTHTHHHTH...or you might hear THTTTH THHTTHTHTTTTTHHHTHTHTH. . . , and so forth. Consider the set of all possible outcomes of their flipping (all possible sequences of H's and T's). Does the set of possible outcomes have the same cardinality as the natural numbers? Justify your answer.

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 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 at once). Now you give each person a penny; then ask everyone to flip his or her penny at the same time. Then ask them to shout out in order what they flipped (H for heads and T for tails). So you might hear: HHTHHTTTHTTHTHTHTHHHTH...or you might hear THTTTH THHTTHTHTTTTTHHHTHTHTH. . . , and so forth. Consider the set of all possible outcomes of their flipping (all possible sequences of H's and T's). Does the set of possible outcomes have the same cardinality as the natural numbers? Justify your answer.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

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 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 at once). Now you give each person a penny; then ask
everyone to flip his or her penny at the same time. Then ask them to shout
out in order what they flipped (H for heads and T for tails). So you might
hear: HHTHHTTTHTTHTHTHTHHHTH... or you might hear THTTTH
THHTTHTHTTTTTHHHTHTHTH. ., and so forth. Consider the set of
all possible outcomes of their flipping (all possible sequences of H's and T's).
Does the set of possible outcomes have the same cardinality as the natural
numbers? Justify your answer.

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