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# What is the difference between 'Equals' and iff? watch

1. (Original post by LJoll)
Well one of them implies that two things are exactly the same and the other says that one things can only be true if the other is true, but does not necessitate any specific relationship between the properties of the two things.
That's not quite what iff says. A iff B means that "A is true whenever B is true, and false whenever B is false, and vice-versa". That sounds very much like the sort of equivalence that "equals" also indicates to me. On the contrary; "A iff B" indicates that A and B are dependent to the point of having all the same properties.
2. (Original post by generalebriety)
That's not quite what iff says. A iff B means that "A is true whenever B is true, and false whenever B is false, and vice-versa". That sounds very much like the sort of equivalence that "equals" also indicates to me. On the contrary; "A iff B" indicates that A and B are dependent to the point of having all the same properties.
Yeah, that was a really lazy definition I gave.

I think the main difference is that "A iff B" doesn't necessitate any correspondence of their properties. "=" does.
3. If anyone still cares, seven months later, about this question, my new lecturer has (rather promptly) provided an answer to this question. He explained that the difference is this: <-> is a propositional connective between two sentences, but = is a binary predicate between two objects. So, for our example, 2+2=4 because 2+2 is an object (or, rather, an object formed from a function symbol acting on two objects), and 4 is an object, but 2+2=4 is a sentence (because a sentence must have both objects and predicates - in this case the predicate is =).

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Updated: January 5, 2009
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