The subset Re (real numbers) of complex numbers is neither open nor closed. A neighborhood around any real number x in the complex plane, defined as {z | |z - x| < δ}, contains non-real numbers, confirming that Re is not open. Additionally, since the closure of Re includes all real numbers and does not include any non-real numbers, it is also not closed. This conclusion is based on the properties of open and closed sets in topology.
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Let x be any real number and consider a neighborhood of it in the complex numbers: \{z | |z- x|< \delta\}. Does that contain any non-real numbers?Fairy111 said:Homework Statement
I need to find out whether the subset Re(real no's) of complex no's is open, closed or neither.
Homework Equations
The Attempt at a Solution
Im not really sure how to begin this...any help please?