# Questions tagged [notation]

For questions about good use of notation, comparison of specific notation, motivation of notation.

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### Do students confuse $\log_ab$ and $\log a^b$?

I recently observed a group of students being introduced to logarithms for the first time. Some of them had trouble writing $\log_ab$ properly, and it looked more like $\log a^b$. All logarithms have ...
896 views

### Why is multiplication taught using cross notation at first?

Alert: I am not a math educator. It seems to me that multiplication is first taught using the cross notation, for example $3\times 5=15$. First question - is that even correct? Maybe not all schools ...
585 views

### Is using different notations in one course a good idea?

From aesthetical point of view, using two symbols for the same concept during the same course is obviously a very bad idea. However, especially when I teach freshmen, I often deliberately mix ...
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### Explaining the symbols in definite and indefinite integrals

I teach the definite integral before the indefinite for a few reasons, one of which is that I want students to recognize that the definite integral means area (not anti-derivative). If we do ...
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### The use of "$\therefore$" and "$\because$"

In schools, many students learn the usage of "$\therefore$" and "$\because$" in proofs. Such three-dot notation are popular in many high-school books and exams, but are almost ...
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### As a TA, how to reduce imprecise notations/statements in students' exams

I'm not a course instructor, just a TA of the first quarter calculus course who lead discussion sections and grade exams. When grading the midterm, I found large number of students showed some ...
492 views

### Using $dx$ for $h$ in the definition of derivative

Is it mathematically correct to write $$f'(x)=\lim_{dx\to0}\frac{f(x+dx)-f(x)}{dx},$$ rather than $$f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}?$$ If not, what is the difference? If so, why isn't this ...
1k views

### Writing Fractions "Correctly"

I very often see students writing, for example, $1/3x$ when they mean $\frac 13x$. I used to tell them not to write $1/3x$ beause it looks like $\frac{1}{3x}$ until I realized that, according to ...
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### Proof of why BODMAS (or BIDMAS) works?

In my first full-time teaching post, it is very likely that I'll need to be teaching a small amount of GCSE Mathematics to students retaking it. One thing that has been bugging me is that I can't seem ...
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### How to teach brackets?

I was taught in a school that one has to use different brackets in expressions like $\{[(3+4)\cdot 4]^4\}^{1/2}$ to denote the order which subexpression is evaluated first. But can this be recommended ...
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### Why do some of my, usually international/Indian students, write limits to the left of the integral?

I see a lot of my students (I am in the US), usually Indian, write the limits of integration to the LEFT of the integral sign rather than customary top or right. The formula will look for example like ...
867 views

### Multiple students writing $y\frac{d}{dx}$ rather than $\frac{d}{dx}y$ -- why?

I'm currently teaching a couple of courses that have a calculus prerequisite, and within the last week I've had two students make notational mistakes that amount to writing $y\frac{d}{dx}$ rather than ...
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### Are there any negative consequences in applying operations/functions to a whole equality?

Some of my students solve equations not by applying the same operations on the left and right sides of an equation, but by applying the operation to the whole equality. For example, they may write ...
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Today in second semester calculus, I found myself stumbling a bit to provide a natural-sounding explanation for all the letters involved in the expression $$\lim_{t \rightarrow \infty} \int_1^t \frac{... 1answer 934 views ### How to denote angle? I'm teaching mathematics on my free time for young pupils. Once I have seen that they denote angles like \angle ABC. But sometimes I have difficulties to understand whether they mean an angle or its ... 6answers 2k views ### What is the right notation to use in multivariable chain rules? The following "chain rule" is in my multivariable calculus course: If f depends on x and y, but x and y depend on t, then \frac{df}{dt} = \frac{\partial f}{\partial x} \frac{d ... 5answers 1k views ### A different symbol for the indefinite integral/antiderivative? Examples. An indefinite integral (or antiderivative) of \cos is \sin:$$\int \cos = \sin.$$Edit: There has been much unexpected confusion with the above statement. I define the above statement ... 3answers 386 views ### Framework for Compound Inequalities I have been presenting compound inequalities like 3 < x < 7 as being a shorter way of saying 3 < x and x < 7. From this point of view, though, I end up having to admit that ... 2answers 608 views ### Is this example of Leibniz notation sloppy? In helping a family member who is studying calculus, I was asked about the meaning of the following, which is straight out of a calculus text book (Varberg and Purcell) v'(t) = \frac{{\rm d}\,v}{{\... 2answers 4k views ### Notation of points with coordinates At least in Germany, nearly all teachers and textbooks use the notation$$P(x,y)$$for the point P with coordinates x and y. My own math professors at university always cried about this, as the ... 1answer 8k views ### When and Why are different division symbols taught? There are 4 division symbols that I have learned/taught. Below is 18 divided by 3, shown with 4 different symbols. This question was sparked by the comments on my answer to the question on examples ... 6answers 432 views ### Helping high school students remember inequalities and division Background I sometimes tutor high school students and I have come across various problem types that are best represented by the following two problems. They are unable to keep track of the correct ... 2answers 532 views ### Fear of notation and hazily-appeared writing in Mathematics I am looking for literature related to fear of notation in mathematics. It is even heard that the font size and font type make a reader reluctant to study mathematical literature, often lecture notes,... 1answer 303 views ### Terminology for parts of limit notation When we talk about:$$\lim_{x\to{c}}f(x)=L Is there a formal name for the number "$c$"? I know of course that it means "$L$ is the limit of $f(x)$ as $x$ approaches $c$". It just would be nice to be ...
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In the textbook I am using to teach mathematics to high school students I found the following illustration about composition of functions. I do not agree with this illustration. For me $g$ is the ...
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### In teaching mathematics, should one always follow some international standards such as ISO 80000-2?

ISO 80000-2:2009 is a standard describing mathematical signs and symbols developed by the International Organization for Standardization (ISO). In teaching mathematics, should one always follow this ...
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### Teaching asymptotic notations at the beginning of calculus [duplicate]

I'm thinking about teaching calculus by firstly introducing the asymptotic notations (big-Oh, little-oh, and $\sim$), secondly explaining their "arithmetic" (things like how to sum little-oh's and ...
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### Notation for change of basis matrix

As far as I can tell, it's only a slight exaggeration to say that every text has a different notation for a change of basis matrix from (say) $\mathcal{B}$ to $\mathcal{C}$. That's not even to talk ...
245 views

### What symbol is appropriate to represent a sum modulo N? [closed]

I am writing a blog post about cryptography and I need to show some examples that involve sums modulo N. I would like (if possible) to use a different "plus" symbol for these sums. The kind of ...
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### Is "hat notation" for unit vectors commonly used in mathematics?

As an undergraduate, I clearly remember learning and using "hat notation" to describe unit vectors. That is, if $\vec{v}$ is any vector (in 2 or 3 dimensions) then $\hat{v}$ denotes the unit vector ...