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1. You can either meet me at home or at the office.

2. You can meet me either at home or at the office.

I know #2 is grammatically correct, but I read #1 as an example sentence in a grammar book. Is #1 acceptable and grammatically correct?

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Strictly speaking, #1 is not properly formed. In reality, however, some people would say #1 in everyday language, and it might not be noticed as an error. To be formally correct, especially in writing, you should use #2.