I got an email from an instructor today. Towards the end of email she says:
"Here is to finishing off the semester in a positive way."
What does that mean?
"Here's to ..." is a phrase used when making a toast. It means "Here is a toast to ...", at which point it is customary to raise your glass. The phrase has a life of its own, used by a speaker or writer expresses a situation that calls for a toast-like salute to something.
The "Here is" part can be omitted also. For instance, the wording of a toast may simply be something like, "To your health!"
The preposition or particle "to ~" in this situation means something like: "for the sake of the (continued) good status of ~" or "in recognition/appreciation/celebration/congratulation of ~" or "in hope of ~"
It is a way of expressing a wish for success. In other words: "I hope you will finish off the semester in a positive way".
"Here is to..." or "Here's to..." is a friendly way of saying "I am looking forward to..."
Another example: A salesman may say at the end of the year: "Here's to another great year of sales"
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