The preposition is an invariable part of the sentence that establishes a relation between two words. They don't have a meaning of their own and show position, time, relationship, etc. between words.
Examples of the construction preposition + infinitive are shown below:
Ella sigue sin mirar atrás.
She keeps going without looking back.
Él salió sin decir adiós.
He left without saying goodbye.
Yo tengo un boleto para viajar.
I have a ticket to travel.
Yo camino al restaurante para cenar.
I walk to the restaurant to have dinner.
Tomamos café después de cenar.
We drank coffe after having dinner.
Yo solía ir a correr todas las mañanas.
I used to go jogging every morning.
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