Purpose with for + verb-ing and to + infinitive

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For + verb-ing
We use 'for + verb-ing' to talk about the function of an object. It's used when we want to explain what something is generally used for or what its purpose is. We DON'T use 'for + infinitive'.

  • A camera is for taking photos. (NOT: for take photos.)
  • The headphones are for listening to music.
  • What's this for? (= what does this do / what is the function or purpose of this object?)
  • This knife is for chopping onions.
When the subject of the sentence is a person, and we are talking about the function of an object, it's also possible to use 'to + infinitive', as well as 'for + verb-ing'.
  • I use this box to store DVDs.
  • I use this box for storing DVDs.
To + infinitive
When we want to talk about someone's intention or goal, about why they are doing something, we need to use 'to + infinitive'. In this case, the subject of the sentence is a person.
  • I went to London to study English. (NOT: for studying / for study.)
  • I'm going home to relax. (NOT: for relaxing / for relax.)
  • She sat down to read.
  • He went to the library to study.
For + noun
We can also use 'for' with a noun (NOT with verb-ing) to talk about someone's intentions or goals.
  • I went to the shop for milk.
  • I went to the shop to buy milk.
  • NOT: I went to the shop for buying milk.
  • NOT: I went to the shop for buy milk.
In order to
We can use 'in order to' or 'so as to' instead of 'to + infinitive'. This just makes it a bit clearer that we are talking about goals or intentions and it's also a bit more formal. It doesn't change the meaning.
  • I went to London in order to study English.
  • I went to London so as to study English.
Verb patterns
Some verbs (or adjectives or nouns) need 'to + infinitive' or 'for + verb-ing' as part of their patterns. This is different from the uses I've talked about above, because here we are not always talking about purpose. 'To + infinitive' and 'for + verb-ing' don't have a special meaning when they are part of a verb pattern. It's just that this construction always follows this verb or adjective. These are some examples, but there are many more.
  • Decide + to + infinitive: I've decided to go home.
  • Promise + to + infinitive: She promised to arrive early.
  • Ask someone + to + infinitive: John asked Lucy to pass the salt.
  • Want + to + infinitive: I want to buy a new coat.
  • Be sorry + for + verb-ing / noun: I'm sorry for breaking your vase.
  • Apologise + for + verb-ing / noun: He apologised for forgetting about the meeting.
  • Thank someone + for + verb-ing / noun: Thank you for helping me.
  • Reward someone for + verb-ing / noun: The police rewarded him for finding the stolen car.
Try an exercise about using 'for + verb-ing' and 'to + infinitive' here.