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Enumeration
Take a look at the following sentences and tell me if I should use the gerund form:
His passion for the trips, for the scientific and technological advances will be constant in his life.
To see (Seeing) the world, and also to understand (understanding) the world. To talk about (talking about) life. To listen and to speak (listening and speaking); the social gatherings...
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Re: Enumeration
Yes. It isn't wrong to use the infinitive, but the gerund sounds more "normal". Guessing at the other context, I’d say:
His passion for excursions and for scientific and technological advances is a permanent part of his life: seeing and understanding the world, talking about life, listening and speaking, the social gatherings…
It was always his desire to see the world.
Seeing the world was always his desire.
I guess if it comes first, you usually use the gerund, and if second the infinitive, but you can certainly say:
To see the world was his desire, to understand the world, his fantasy.
"It was always his desire seeing the world" doesn't work. It makes it sound as if something not mentioned here were his desire while he was seeing the world.
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Re: Enumeration
Both the gerund and infinitive are completely fine here grammatically, but I prefer the gerund stylistically (although others may disagree).
However, I would suggest some very minor modifications to the rest of your writing (I understand you are going for dramatic, choppy phrases)
His passion for the trips, for the scientific and technological advances, will be constant throughout his life.
To see (Seeing) the world, but also to understand (understanding) it. To talk about (talking about) life. To listen and to speak (listening and speaking); the social gatherings...