Identifying if A is Open or Closed

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The discussion revolves around determining if the set A, defined as A={z | I am z > 1}, is open or closed. Participants express uncertainty about applying the definition of an open set to this specific case. Clarification is sought regarding the definition of an open set and examples that illustrate why certain sets are classified as open. The comparison is made to set B, which includes all points in the plane where y > 1, suggesting a similar analysis may apply. Ultimately, the conversation emphasizes the need for a clear understanding of open sets in mathematical contexts.
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Homework Statement



For the following set, state and justify whether or not it is open or closed.

Homework Equations



A={z| I am z >1}

The Attempt at a Solution



I know the definition of an open set, but I am not sure how to use it to solve this question.
 
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What is you definition of open set? Do you know some examples of open sets and why they are open? This shouldn't be that challenging. It's the identical to asking if the set B of all points in the plane with coordinates (x,y) with y>1 is open.
 

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