Discussion
What does the equality symbol assert in first order logic?
Answer: D
Equality relates terms and asserts identity of the objects they denote, which is why it permits substitution and why counting statements can be written. Truth value equality is equivalence between formulas, indiscernibility is a consequence rather than the definition, and syntactic identity is a different relation entirely. Having identity available in the logic is what allows uniqueness and cardinality to be expressed at all. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.
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