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

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The discussion revolves around understanding the relationship between sets and elements, specifically in the context of a problem involving frogs. The user is confused about the notation and the meaning of sets, particularly how elements like "toadie" relate to the set of frogs. They express uncertainty about the interpretation of "frogs(f)" and whether it implies that a set can contain another set as an element. The conversation highlights a need for clarification on set theory concepts, particularly the distinction between elements and subsets. Overall, the thread seeks to demystify the relationship between sets and their elements in a straightforward manner.
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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