What Does ##n(A)## Represent in Set Theory?

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In set theory, ##n(A)## represents the number of elements in set A, regardless of their names. The discussion clarifies that the identity of the elements does not affect the count; for example, sets {1, 2, 3} and {a, b, c} both contain three elements. The confusion regarding whether to count elements as distinct based on their names is addressed, confirming that names are irrelevant for determining the count. Ultimately, the number of elements in a set is what matters, not their labels. This understanding resolves the initial doubts about the value of ##n(A)##.
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Homework Statement


attachment.php?attachmentid=70965&stc=1&d=1404035528.png

##n(A)##
I have some doubts.
Obviously, ##n(A)## means the number of elements in set A.
Should it be 3 or 6?

Should I consider each number to be a different element?
 

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The names of the elements are irrelevant. If you change the names ##\{1,2,3\}## by ##\{a,b,c\}##, then it will have the same number of elements. Does that answer your question?
 
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micromass said:
The names of the elements are irrelevant. If you change the names ##\{1,2,3\}## by ##\{a,b,c\}##, then it will have the same number of elements. Does that answer your question?
Yes, thank you :smile:
 

Thread 'Find the polar form of a complex number'

The working out suggests first equating ## \sqrt{i} = x + iy ## and suggests that squaring and equating real and imaginary parts of both sides results in ## \sqrt{i} = \pm (1+i)/ \sqrt{2} ## Squaring both sides results in: $$ i = (x + iy)^2 $$ $$ i = x^2 + 2ixy -y^2 $$ equating real parts gives $$ x^2 - y^2 = 0 $$ $$ (x+y)(x-y) = 0 $$ $$ x = \pm y $$ equating imaginary parts gives: $$ i = 2ixy $$ $$ 2xy = 1 $$ I'm not really sure how to proceed from here.
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