Я хочу запомнить это событие навсегда.

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Breakdown of Я хочу запомнить это событие навсегда.

• это: this
• хотеть: to want
• запомнить: to remember

Questions & Answers about Я хочу запомнить это событие навсегда.

Why is the verb запомнить used here instead of запоминать?

Russian verbs come in pairs of aspects: perfective and imperfective.

• запомнить is perfective, meaning the action will be completed (i.e. you will successfully commit it to memory).
• запоминать is imperfective, focusing on the process of memorizing without guaranteeing completion.
  Since you want to express a one-time, completed act of remembering, you use the perfective запомнить.

What case is это событие, and why does it look like the nominative?

это событие functions as the direct object of запомнить and is therefore in the accusative case.

• For neuter nouns like событие, the accusative form is identical to the nominative.
• это here is a demonstrative pronoun (neuter singular) that also remains unchanged in the accusative.

How does the structure хочу + infinitive work in Russian?

In Russian, to express desire you use хотеть (to want) followed by an infinitive:

• Я хочу читать – “I want to read.”
• Я хочу запомнить – “I want to remember.”
  This is a straightforward pattern: subject + хочу + infinitive.