66

In math and computer programing, variables and constants (such as x and t in your examples) are treated like proper nouns (like names of people or places) rather than common nouns (names of a type of object). Just as you wouldn't say "I wonder what the Bob is doing today?" or "The Mary is coming over for dinner tonight." you also wouldn't ...


40

Of course in most contexts we use a to refer to a generic, non-specific example of some class (or the first mention of a specific member of that class), and the to refer to a specific previously-mentioned member of that class. This is not the case here. In this usage, both a and the can be used to describe an exemplary peasant, taking some random peasant in ...


15

We can use the indefinite article (a peasant) if we are discussing an unknown peasant, or the definite article if we are discussing the generic peasant (considered as a type of person). Either is appropriate in the context you quoted.


13

It’s a matter of context, and to a lesser extent jargon. A variable in mathematics actually has nothing to do with the symbol or name used to identify it. x² + y³ = 0 will always have the same solutions regardless of whether the variables are identified as x and y, Α and Β, or even ζ and Д. However, in any given form of an equation, the symbol or name used ...


6

In both cases, you’re using ’peasant’ as a generic, but the generic forms are different in their meaning. A generic formed with the definite article in English is generally categorical. In other words, it talks about the noun as a category of person/place/thing/idea, describing all items referenced by that noun as one group. This is essentially the same as ...


5

I sometimes hear articles in front of a variable name, if it’s to distinguish which of several possible assignments we mean. For example, if we have a sequence whose elements are a-sub-0, a-sub-1, and so on, I might specify “The a-sub-i minimizing the difference between a-sub-i squared and v,” or “an a-sub-j satisfying the inequality, ....” Afterwards, I ...


4

The complete noun phrase is "train rides." So your question is ultimately about the use of articles with rides. We do not use "a" with a plural noun. We do not use "the" with the first mention of a plural noun. If a noun refers to a plurality of things that can be understood from context, then you may use "the." ...


3

There are many kinds of "accidents". A "car" accident is just one of them. So it would be unnatural to use "the car" right off the bat. In fact, even if the first sentence was about a "car" accident, it would still be awkward to use "the car" in the second sentence: I saw a car accident this morning. ??The ...


3

I believe the reason can be demonstrated with an example: Solve 7x² + 13x = 9 for the x. Which one? The first x or the second x? Solve 7x² + 13x = 9 for an x. So I can just pick either one? Here you go: x = (9-7x²)/13 This is of course not the solution most people are expecting. The point being, there are two things here: A quantity, which we have ...


3

Nouns are often described as being a person, place, or thing, but that's not quite correct. Common nouns actually are category labels. For instance, the word "book" labels the category of books. In English, simply referring to "book" is not grammatical, because "book" does not refer to a thing but a category. We need a ...


3

This is a use of the definite generic article; we mean "in heads in general". Saying "a pain in a head" implies that there are many possible heads you have that might have pains in, because the indefinite article means "one nonspecific member of all X". We tend to use the definite generic for body parts, like (Corns and ...


3

This is a difference of dialect. People say “a” before a breathy H but “an” before a silent H. Jane Austen spoke a dialect where the H in heroine was silent. I personally would say, “a heroine,” but “an herb,” or “a house” but “an hour.” That said, “a heroine” is much more common today, and “an hero” would make me think of an offensive meme, rather than ...


3

Both are grammatically valid. "Male" and "female" can be used as either nouns or adjectives. As a noun, one might say, for example, "Three males entered the room." As an adjective, one could say, "Male peacocks have fancy tails." Note "male" here is an adjective modifying "peacock". So you could say,...


2

The option "in the way" suggests that there is only one standard, well known way of applying pressure. The option "in a way" suggests that there could be multiple ways in which the pressure could be applied.


2

The word thing is countable, so it always needs an article (a thing, the thing) or a determiner (my thing, John's thing, etc.) Therefore the sentence is incorrect if you try to remove the article, like There is not even single thing... because single is an adjective, not a determiner. You could remove the adjective single and make it There is not even a ...


2

There are a few options, and some can be slightly emphasised: without help from without any help from with no help from without the help of Here is the order in which they are commonly preferred (if you click on the image it will be enlarged): Although NGram finds instances of without the help from, it is very rare and I wouldn't recommend it. One more ...


2

Both constructs are acceptable. However, there can be a difference in interpretation. 'A peasant' uses peasant as a generic category: that class of people known as peasants. 'The peasant' may also use peasant in this generic, categorical sense. However, 'the peasant' might also refer to a particular, singular person: 'The Peasant, name unknown, social caste -...


2

The character Twain was writing about, Pudd'nhead Wilson, is trying to define courage by giving examples of what it is and what it isn't. Courage IS resistance to fear Courage IS mastery of fear But courage IS NOT absence of fear He goes on to give the example of the flea, a tiny, fragile, creature that lives on creatures that are much bigger and stronger ...


2

Both are correct. If Google Ngrams can be believed, "served as chairman" has been more common for a long time. But be aware that "chairman" may have sexist connotations. Unless you have a good reason not to do so, I recommend "served as chair." Google also indicates that this genderless version has gained popularity in the last ...


1

"Train" is a noun, but it's not the noun. We're talking about rides on trains -- and "trains" is plural in that phrasing.  The reason that it isn't plural in the phrase "train rides" is that it is attributive.  It's job in that phrase is a role that's more typically filled by adjectives. In other languages, adjectives have ...


1

The is a determiner - basically a demonstrative adjective - the means "that exact/particular noun of which we (speaker and listener) are [now] aware.” (The is similar to “that” - in fact it is a form of the Old English “that” and often “that” can be used in place of the.) The is used (i) where the noun is well known to everyone: "The moon is ...


1

"The" is used when the reader knows exactly what it's talked about. So it's shared information between both the writer and the reader. However, in this sentence, "a" is used in "a small house" and in "a village" because it could be any house in any village located in the Netherlands, the reader doesn't acknowledge this....


1

You would use a if you are referring to one of many possibilities, for example: The phone switches to a network with a stronger connection than the current one. This sentence suggests that there might be multiple connections that are stronger than the current network, and the phone could switch to any of those networks. We use the when there is only one ...


1

You use the definite article (the) when you are referring to something specific. Context is everything, because some things can be unique in one context but not in another. For example, there are lots of cars in the world, so one might say "I own a car", but English speakers often refer to the car that they own as "the car", because it is ...


1

"the" in this case would refer back to a set of photos that were already specified. E.g. "Once I uploaded all my vacation videos and photos, the site made organizing and viewing the photos in groups a snap." If referring to photos in general, do not use "the": "The site made organizing and viewing photos in groups a snap....


1

"I request you to change the color of the book cover from the blue to the white." The entire sentence, as written, sounds wrong; however, using an article with colours in similar contexts can be correct. You can abbreviate statements about things if you have previously stated certain details already. For example, if a restaurant menu had beef ...


1

You are right that the patio is quite specific, but you use the only when both speaker/writer and listener/reader know, or can reasonably guess, which one you are talking about. For example, if you are at a restaurant, you might say: Let's have lunch on the patio. What makes this sentence different is that, when we use the expression there is to introduce ...


1

In this case, it appears that you're describing an ID which has previously been mentioned (which I'm inferring from the use of 'current'). Therefore, I would suggest using 'the', to make the sentence: ..., where id is supposed to contain the current vendor ID. (also note the capitalisation of 'ID', as an abbreviated form of 'identification' or 'identifier) ...


1

I do not see anything ungrammatical about we have reached a main result of ... Indeed in some contexts use of "the" instead might be incorrect. Computer grammar checkers are not yet good enough to be relied on for decisions, in my view. The most they are good for is to highlight text for human examination and decision.


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