(See Steps) (a) Give the definition that a set is open. (b) Use the definition to prove that the set A=x ∈ R \mid x ≠q 0 is open (c) Use the definition
Question: (a) Give the definition that a set is open.
(b) Use the definition to prove that the set \(A=\{x \in \mathbf{R} \mid x \neq 0\}\) is open
(c) Use the definition to prove that the set \(B=\{x \in \mathbf{R} \mid 0 \leq x<1\}\) is not open.
Deliverable: Word Document 
![[Solution Library] (a) Let S subet; R.](/images/solutions/MC-solution-library-53117.jpg "[Solution Library] (a) Let S subet; R. Prove that if x ∈")
[Solution Library] (a) Let S subet; R. Prove that if x ∈
![[Solution Library] (a) Use the \epsilon-N definition](/images/solutions/MC-solution-library-53118.jpg "[Solution Library] (a) Use the \epsilon-N definition to prove lim _n")
[Solution Library] (a) Use the \epsilon-N definition to prove lim _n
![[See Steps] Find the limit that exists.](/images/solutions/MC-solution-library-53119.jpg "[See Steps] Find the limit that exists. (a) lim _n \rightarrow+∞")
[See Steps] Find the limit that exists. (a) lim _n \rightarrow+∞
(Steps Shown) (a) Give the definition that a sequence a_n is Cauchy.
(Step-by-Step) Assume that f is defined on (-1,1) and is continuous
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