I know this seems like a silly question, but someone was trying to debate with me about how $2+2=4$ should be called an identity and not an equation. I mentioned how it has no variables and isn't true for all numbers, but they claimed you could plug in any value for its variables(which don't exist) and it would be true and so is an identity. Which is kind of true in a round about way, but I still don't think anyone would call it an identity in a casual situation.
Is $2+2=4$ an identity?
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13It's both an equation and an identity, but not a particular interesting example of either. – 2012-03-21
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3To clarify, as I understand it *equation* refers to the form of the logical statement, while *identity* refers to the truth of the statement itself. – 2012-03-21
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1So they're saying $1 = 1$ is actually $$\forall x,y,z,w,u,v,\ldots (1 = 1)$$ Hm.. – 2012-03-21
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0This is [somewhat related](http://math.stackexchange.com/questions/95069/how-would-one-be-able-to-prove-mathematically-that-11-2/95070#95070). – 2012-03-21