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Problem 12.1.6. Show that each of the following sets countable. (a) {2,3, 4, 5, ...} = {n}2 (b) {0, 1,2, 3, ...} = {n}o (c) {1,4,9, 16, ...,n²,..} = {n²},, n=1 (d) The set of prime numbers (е) Z

Problem 12.1.6. Show that each of the following sets countable. (a) {2,3, 4, 5, ...} = {n}2 (b) {0, 1,2, 3, ...} = {n}o (c) {1,4,9, 16, ...,n²,..} = {n²},, n=1 (d) The set of prime numbers (е) Z

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Real math analysis, Please help me solve problem 12.1.6

Definition 12.1.4. Any set which can be put into one-to-one correspondence {1,2, 3, ...} is called a countably infinite set. Any set which is either with N finite or countably infinite is said to be countable. Since N is an infinite set, we have no symbol to designate its cardinality so we have to invent one. The symbol used by Cantor and adopted by mathematicians ever since is No. Thus the cardinality of any countably infinite set is No. N is the first letter of the Hebrew alphabet and is pronounced "aleph." No is pronounced "aleph null." %3D We have already given the following definition informally. We include it formally here for later reference.
Transcribed Image Text:Definition 12.1.4. Any set which can be put into one-to-one correspondence {1,2, 3, ...} is called a countably infinite set. Any set which is either with N finite or countably infinite is said to be countable. Since N is an infinite set, we have no symbol to designate its cardinality so we have to invent one. The symbol used by Cantor and adopted by mathematicians ever since is No. Thus the cardinality of any countably infinite set is No. N is the first letter of the Hebrew alphabet and is pronounced "aleph." No is pronounced "aleph null." %3D We have already given the following definition informally. We include it formally here for later reference.
Problem 12.1.6. Show that each of the following sets countable. (a) {2,3, 4, 5, ...} = {n}2 (b) {0, 1,2, 3, ...} = {n}o (c) {1,4,9, 16, ...,n²,..} = {n²},, n=1 (d) The set of prime numbers (е) Z
Transcribed Image Text:Problem 12.1.6. Show that each of the following sets countable. (a) {2,3, 4, 5, ...} = {n}2 (b) {0, 1,2, 3, ...} = {n}o (c) {1,4,9, 16, ...,n²,..} = {n²},, n=1 (d) The set of prime numbers (е) Z
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