Please, someone help me about the differences between "TO" and "FOR" When we use "to" and "for"
e.g. My English goal for July 9th, 2015 is to increase my vocabulary. (why we use "VERB TO BE" and "TO")
Why is not correct to use:
e.g. My English goal TO July 9th, 2015 is FOR increase my vocabulary.
For confusing things like this, I really recommend just following the example instead of analysing it too much. The problem is, both <em>to</em> and <em>for</em> have about twenty meanings each, depending on context. Look too closely and you'll just become lost.
Anyway, I'll try to explain a little bit.
<em>My English goal for July 9th, 2015</em> - this means your plan on that day, or what you plan to do when that day comes. <em>To</em> will change the meaning and it will (awkwardly) sound like "until". Remember that <em>to</em> can mean a transit somewhere or somehow - movement or change.
We use <em>is</em> because we understand the message as, "My English goal is..."
Verbs in the infinitive form (<em>to increase</em>) can mean an intention or an action you wish for. An expanded vocabulary is what you want, so <em>to increase</em> tells us your intention. "For increase" is simply wrong. If you have a preposition (apart from <em>to</em> - more rules for that!) the action that follows must be in a gerund form, so <em>for increasing</em> is technically correct. However, now the sentence changes meaning again (and sounds awkward again), because we use <em>for (verb)ing</em> to mean an existing purpose.
So as I said, it's far easier to just accept the example as correct and follow that pattern.