Timeline for How do you read these mathematical expressions aloud?
Current License: CC BY-SA 3.0
20 events
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| Sep 6, 2019 at 20:36 | comment | added | Michael Bächtold |
Again: 1/(x+1)sqrt x is not a full description of a function. A full description would be x |--> 1/(x+1)sqrt x, using mathematical notation. Using python notation the same might be written as lambda x:1/((x+1)*sqrt(x)). Unfortunately, not only English-speakers are quite happy to do what you are suggesting. In German, Italian, French etc. people do the same. This has historical reasons, but mathematically it's wrong, if we stick to the modern definition of "function".
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| Sep 6, 2019 at 16:23 | comment | added | Jasper | @MichaelBächtold -- Either you are making a distinction that the English language does not make, or English-speakers are quite happy to use a complete description of the implementation of a function as a name for that function. | |
| Sep 6, 2019 at 6:41 | comment | added | Michael Bächtold | I fully agree with that definition. So when we write f(x) = 1/(x+1)sqrt x , then f is the function, and not f(x). Hence 1/(x+1)sqrt x cannot be the function since it is the same as f(x). But again: that is the modern definition. For 200 years it was correct to say f(x) is a function of x, or 1/(x+1)sqrt x is a function of x etc. | |
| Sep 5, 2019 at 18:26 | comment | added | Jasper | @MichaelBächtold -- Here is the technical definition I am using: "A function f from a set X to a set Y is a correspondence that assigns to each element x of X a unique element y of Y. The element y is called the image of x under f and is denoted by f(x). The set X is called the domain of the function. The range of the function consists of all images of elements of X." Swokowski's next sentence is, 'The symbol f(x) used for the element associated with x is read "f of x."' | |
| Sep 5, 2019 at 11:07 | comment | added | Michael Bächtold | Actually, Collins 5th is not the same as its 4th definition of function. The 5th is about "function of" which is not defined in modern mathematics and not the same as a mapping. This is precisely the distinction of the pre- and post 1930 definition of the word "function" in mathematics. See the link in my first comment. | |
| Sep 5, 2019 at 11:01 | comment | added | Michael Bächtold | I wouldn't trust an English dictionary to give a precise definition of a mathematical term. 1/(x+1)sqrt(x) is not a mapping, since it doesn't come with the information of what the input variable is. You might think it's obviously x, but what if we had previously declared that x=t^2. Then 1/(x+1)sqrt(x)=1/(t^2+1)|t|. The left and right hand side are equal, but are they the same mapping? What is the input variable of this object? | |
| Sep 5, 2019 at 6:48 | comment | added | Michael Bächtold | If we stick to the official (modern) usage of the word "function", then saying "the function is one divided by x ..." is not correct, since 1/x is not a function. It would have been correct in pre 1930 mathematics. Some details on the history can be found here. | |
| Apr 14, 2016 at 4:18 | comment | added | user3932000 | This is really, really wordy, and very few people will actually read it like this. | |
| May 26, 2015 at 18:35 | comment | added | Ben Kovitz | @Munchkin Actually, "limit" is just līmes imported into English in the usual way, making the stem into a word on its own rather than using the nominative. | |
| Dec 15, 2014 at 12:56 | comment | added | Munchkin | offtopic: nice to know that you call it "limit". In germany we say "limes" (see: en.wikipedia.org/wiki/Limes). Until now I thought "lim" stands for "limes" and everyone in the world call it so :-D | |
| Dec 14, 2014 at 18:11 | history | edited | Jasper | CC BY-SA 3.0 |
Responded to J.R.'s suggestion.
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| Dec 14, 2014 at 11:17 | comment | added | J.R.♦ | I think "approaches" can also be used in lieu of "goes to". | |
| Dec 14, 2014 at 8:07 | comment | added | Jasper | I was taught to use the term "sum" for discrete sums, such as when the (capital) "sigma" notation ( "𝚺" ) is used. I use the term "series" to refer to the sequence generated by evaluating the sum for the various values of n. For example, "1, 2, 3, 4, …" is the sequence of integers. "1, 1/2, 1/4, 1/8, …" is a corresponding geometric sequence. "1, 3/2, 7/4, 15/8, …" is the corresponding series, where each item in the series is the sum of the first i elements of the geometric sequence. | |
| Dec 14, 2014 at 7:59 | comment | added | Jasper | I often say "double integral" when performing either an integral of an integral (such as ∬ a dx dy ) or an area integral (such as ∫ a dA ) or a surface integral (such as ∯ a dA ). Similarly, I often say "triple integral" or "volume integral" when performing either an integral of an integral of an integral (such as ∭ a dx dy dz ) or a volume integral (such as ∫ a dV ). | |
| Dec 14, 2014 at 7:56 | comment | added | Jasper | I was taught to use the terms "integral" and "integration" for the various integral signs (such as "∫", "∬", "∭", "∮", "∯", and "∰"). Similarly, I was taught to use the d notation for full derivatives with respect to a variable, and the partial notation for partial derivatives with respect to a variable. | |
| Dec 14, 2014 at 7:44 | history | edited | Jasper | CC BY-SA 3.0 |
Explained refactorings
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| Dec 14, 2014 at 6:54 | comment | added | Listenever | Don't you ever read 'integral' as 'sum'? | |
| Dec 14, 2014 at 6:53 | vote | accept | Listenever | ||
| Dec 14, 2014 at 2:17 | history | edited | Jasper | CC BY-SA 3.0 |
deleted 6 characters in body
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| Dec 14, 2014 at 2:10 | history | answered | Jasper | CC BY-SA 3.0 |