"Our hope to finish" contains a subject ("Our hope") and an infinitive phrase ("to finish"). The subject is "Our hope," and the infinitive phrase functions as a noun, specifying the desired outcome of the hope.
In the phrase "Our hope to finish," the structure is complex, involving both a subject and an infinitive phrase.
Subject: "Our hope" functions as the subject of the sentence. It is a noun phrase where "hope" acts as the subject, and "our" serves as the possessive adjective indicating to whom the hope belongs.
Infinitive Phrase: "to finish" is an infinitive phrase that functions as a noun, specifically an infinitive used as a noun, often called an infinitive noun. It serves as the direct object of the verb "hope." The entire phrase "to finish" functions as what the hope is directed toward.
So, in this context, "Our hope to finish" can be seen as a subject and its direct object, with the infinitive phrase "to finish" functioning as a noun, specifying the desired outcome of the hope.