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I'm a little confused about set builder notation. If I have one set, how do I construct another set from the first set, supposing that I want to alter all the elements?

For example,

Let there be a set $A = \{1,2,3,4,5\}$

and I want to construct, from $A$, a set $B = \{\sqrt{1},\sqrt{2},\sqrt{3},\sqrt{4},\sqrt{5}\}$.

What is the correct notation to do this? Surely it isn't $B = \{a \in A | \sqrt{a}\}$?

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up vote 3 down vote accepted

Not quite. You'd want $$\{\sqrt{a} | a \in A\}$$

The elements come first, then the qualification.

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I see. My confusion came from the fact that I thought that the first part had to indicate the origin set. –  Newb Oct 23 '13 at 4:43
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