Generate the answer for a given question. The question requires common knowledge of English. Make sure that the answer is in detail, long, consistent with the context, and requires general knowledge of English. To be less repetitive, please vary your language for each question. Give a proper explanation to answer, and if necessary, provide the definition of various terms. And conclude your answer if it's long. If you have used other resources (e.g., Merriam Webster's.) to answer the question, include citations in your answer. You don't need to paraphrase the context of your resources, but make sure that your answer is consistent and complete.

Example Input: Invaluable intuitively seems to imply a higher degree of importance. Please explain the difference between valuable and invaluable and in what context you'd use one or the other.
Example Output: Technically, invaluable works like priceless. They mean that something is of a value which cannot be expressed in numbers. For example great memories, happiness, health, or whatever else you prefer. They are invaluable, because they cannot be sold or bought. They have no price. On the other hand, valuable means something is of a high value, which can be expressed in numbers. Like a golden ring. It's valuable, because it costs $1000.

Example Input: The phrase to boil down to something can be found in most dictionaries. However, to me, it sounds colloquial to write Finding an exact solution to Eq. 1 boils down to ... A real-life example can be found here, and many more here. Interestingly, many of the examples are by non-native speakers. Is it good style to use this phrase in formal writing? (I am prepared to hear that if people use it, then it is OK.).
Example Output: As has been suggested in other answers, it is not very suitable in formal writing. Here are some alternatives you might consider: amount to be reduced to be a matter of be in essence

Example Input: It's a sudden random question I have but I distinctly remember there being another phrase, probably of another language, which means exactly the same as 'word for word'. What is it?.
Example Output:
Verbatim: (from TFD) using exactly the same words; corresponding word for word: a verbatim report of the conversation. or literally: in a literal manner; word for word: translated the Greek passage literally.