N denotes the set of natural numbers and N. denotes the set of non-zero natural numbers. R is the set of real numbers. For A a set, we denote by P(A) its power set. The set of prime numbers is denoted P. Answer the following questions. 4. Let Ak - {k - z|z € N} for k e N° et S = {A} {A2, A3, A4,. Give a description of the set nS and show that there exists a natural number m e N such that m e/ US. Is there another element of N that is not an element of US? Explain your answers.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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N denotes the set of natural numbers and N. denotes the set of non-zero natural numbers. R is the set of real
numbers. For A a set, we denote by P(A) its power set. The set of prime numbers is denoted P. Answer the
following questions.
4. Let Ak - {k - |a € N} tor k e N° et S = {A}2, = {A2, A3, A4,}. Give a description of
the set nS and show that there exists a natural number m e N such that m e/ US. Is there another element of
N that is not an element of US? Explain your answers.
Transcribed Image Text:N denotes the set of natural numbers and N. denotes the set of non-zero natural numbers. R is the set of real numbers. For A a set, we denote by P(A) its power set. The set of prime numbers is denoted P. Answer the following questions. 4. Let Ak - {k - |a € N} tor k e N° et S = {A}2, = {A2, A3, A4,}. Give a description of the set nS and show that there exists a natural number m e N such that m e/ US. Is there another element of N that is not an element of US? Explain your answers.
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