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Questions related to mathematical logic and its use in computer science

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4 answers
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Can I use ellipses in first order logic

I ask, because I have to come up with a first-order logic sentence that shows that there are exactly N objects in the universe. … been able to come up with is: $$ \forall x \; \exists y_1, y_2, \dots , y_{n-1} \; (x \neq y_1) \land (x \neq y_2) \land \dots \land (x \neq y_{n-1})$$ I'm not sure if this is a valid first-order logic
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