Simple set theory question with empty elementsVery simple question, I prob look like an idiot lol. but hey, I'm here to learnso if I have a set A where A = a ∈ N | a 2 = 5 is set A then A = ∅ or is it A = ∅ ?also, if it's the latter, if I have set B say B = 1 , 2 , 3 and want to find the union of A and B, is it { 1 , 2 , 3 } o r { ∅ , 1 , 2 , 3 }? and what about the intersection? if A = ∅ , 1 , 2 and B = 1 , 2 , 3 , then A n B = 1 , 2 right?

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Simple set theory question with empty elementsVery simple question, I prob look like an idiot lol. but hey, I&#039;m here to learnso if I have a set A where   A  =      a    ∈    N          |              a              2              =    5  is set A then   A  =      ∅   or is it   A  =            ∅      ?also, if it&#039;s the latter, if I have set B say   B  =      1    ,    2    ,    3   and want to find the union of A and B, is it   {  1  ,  2  ,  3  }     o  r     {      ∅    ,  1  ,  2  ,  3  }? and what about the intersection? if   A  =            ∅        ,    1    ,    2   and   B  =      1    ,    2    ,    3  , then   A     n     B  =      1    ,    2   right?

Jamarcus Shields · Accepted Answer

Step 1This got a bit long so I will write it here. One way of seeing the notation of sets is what is &quot;in&quot; the curly bracket and the empty set can also be written as   {  } which is notation that is seen. The empty set while not containing anything is itself a thing the same way and empty box is a thing. The set   {  ∅  } is not the empty set the same way a box containing an empty box is not empty. Second notice A must contain natural numbers or rather it is a subset of the natural numbers on the   {  ∅  }  =  {  {  }  } is a set containing the empty set. Step 2Unless you are working with a particular construction of natural numbers done in axiomatic set theory the empty set is not a natural number so the set   {  ∅  } cannot be A simply because it contains an non natural number element

antennense · Accepted Answer

Explanation:If x is any element of   {    a  ∈      N    ∣      a    2    =  5    }, then both   x  ∈      N   and       x    2    =  5. So, is either of these conditions true when   x  =  ∅?

Simple set theory question with empty elements Very simple question, I prob look like an idiot lol.

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