What is the relationship between sets and elements in this problem?

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The discussion revolves around the relationship between sets and elements, specifically using the example of frogs as a set. The user attempts to clarify that if F is a set of frogs and f is an element of F, then f represents an individual frog. The confusion arises when trying to interpret the notation frogs(frogs(toadie)), which suggests that the set containing toadie is also an element of F. The consensus indicates that the terminology used may be misleading and requires a clearer understanding of set theory principles.

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JulianneK
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Hi all I was wondering if you could help me with this problem:

[PLAIN]http://img713.imageshack.us/img713/4306/giflatexl.gif


Could someone explain this relationship in plain english for me please?

[PLAIN]http://img9.imageshack.us/img9/338/codecogseqno.gif

This is what I was thinking, but I think it is wrong:

frogs(f) is a set of frogs where f is an element within the set F. Therefore frogs(toadie) is a set where toadie is an element of F. Therefore frogs(frogs(toadie)) means the set {toadie} is an element of F?
 
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You lost me with the first sentence. Seems to me if F is a set of frogs and f ε F, then f is a frog. So "the set of frogs of f" doesn't make sense to me.

Not being set theory expert, I may be missing something.
 

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