# 4Fun:Worst/Best Notations in Mathematics

1. Sep 19, 2006

### Swapnil

Just for fun (and for my curiosity), what notations/symbols in mathematics do you guys find really annoying or really interesting?

(Please, no whining about the fact that the Greek and the English alphabets look the same :tongue2: We've all been there. )

edit: lets add confusing notations to the mix too.

Last edited: Sep 19, 2006
2. Sep 19, 2006

### CRGreathouse

I was amused by a suggestion at the halfbakery to define ? as the inverse operation to the factorial function. 6?!? = 3.

3. Sep 19, 2006

### matt grime

A notational problem in one sense that annoys me is the usage of p and q as summation indices in the same sum. It's ok in a book, but in a lecture it is annoying. At least p and q are pronounced differently, because even more prevelant is the usage of m and n in the same summation, and a mumbly lecturer with bad hand writing and that choice is a pain in the backside. I made a plan (which I probably forgot to do most of the time) when teaching to always use r, s and t and at most one of n and p as indices in complicated summations ona blackboard. Of course some people managae to have r's that look more like s's.

In a similar vein, and because you should commend the good as well as disdain the bad, I was always thankful to lecturers who adopted such good conventions as putting bars in their z's so they didnt' look like 2's. Very useful in a complex analysis course.

4. Sep 19, 2006

### CrankFan

$${ \cos^{-1} \theta } \over { \sin^{-1} \theta }$$

...I wouldn't say that I find it really annoying. It's just one of those notational things that could lead to confusion.

Last edited: Sep 19, 2006
5. Sep 19, 2006

### Gelsamel Epsilon

$${ \sin^{2} \theta }$$

At one time ages ago I wasn't sure wether it was Sin of the Sin of Theta, or the whole thing squared.

Edit: Interesting to note, I've never had any trouble with greek/english letters. But I have had trouble with m/n like matt said, and also r and v.

Edit2: Also $${ d^{2}y } \over { dx^{2} }$$

Last edited: Sep 19, 2006
6. Sep 19, 2006

### murshid_islam

when i first came across $$f^{-1}(x)$$, i thought it meant $${1}\over{f(x)}$$

Last edited: Sep 19, 2006
7. Sep 19, 2006

### daveb

I always had a problem with people using bold to denote vectors, vector fields, tensors, etc since it's sometimes difficult for someone with my eyesight to tell that something is bold. When they use UPPER case to denote these and lower case to denote these, it's fine, but then you have to deal the vector space V and and an individual vector v in the space.
As for things I like, the Christoffel Symbol, Poisson bracket { } and Commutator [ ] are pretty elegant.

8. Sep 19, 2006

### arildno

1/a. What the heck does the 1/ symbols do there??
Instead, a notation for the multiplicative inverse like $\hat{a}$ is a lot better.
Similarly grumpy about the additive inverse (-1)

9. Sep 19, 2006

### shmoe

Factorial always causes some problems. It's a given that a thread asking why "0!=1" someone will interpret this as "0 does not equal 1". It also makes it more difficult to express suprise and astonishment when an exclamation mark means something else.

I geatly dislike "ln" to mean natural logarithm as well, mostly because it locks people into thinking "log" means "log base 10" to everyone in the world.

10. Sep 19, 2006

### arildno

Gauss detested the factorial notation, so you are not alone!

11. Sep 19, 2006

### matt grime

But the only people who use != to mean not equal to are comp. sci.s, and frankly they will always be confused as long as they use = to mean assignment and == to mean equal. You can't accommodate them no matter how hard you try, which, admittedly, isn't very hard when it's me.

12. Sep 19, 2006

### arildno

Comp. scis are as bad as the electrical engineers with their misuse of the letter "i".

13. Sep 19, 2006

### shmoe

You mean electrjcal engjneers?

My main problem is really people who think the definition or notation they've seen in their first book/course/whatever is always the universal one used by everyone, everywhere and get confused when they find out otherwise.

14. Sep 19, 2006

### Daverz

Gothic letters and script letters, particularly if you can't figure out what letter they are actually supposed to be.

15. Sep 19, 2006

### CRGreathouse

I'm with you on all of those. I think there needs to be some good general notation for iterated functions, distinct from the power notation. I've seen (in Dusart) the use of a subscript for repeated application of a function, but I don't think this is any better.

16. Sep 19, 2006

### Swapnil

So true. I also hate the fat that they use bold letters to denote vectors which is impossible to do when you are writing on a piece of paper. I prefer arrows but those are overused as well.

17. Sep 19, 2006

### Swapnil

You know, I really hate the fact that testbooks usually leave out the $\hat{ }$ (hat) symbol on unit vectors. Now I am getting used to it because usually the only unit vectors we usually work with are $\hat{n}$ and $\hat{t}$, the unit normal and the unit tangent vector, respectively.

Last edited: Sep 19, 2006
18. Sep 19, 2006

### Swapnil

That's why I always use $\arcsin{\theta}$ and $\arccos{\theta}$

19. Sep 19, 2006

### Swapnil

Another notation I hate is the use of $\cdot$ (small dot) to represent dot product. Its looks so much like multiplication! I know, I know ... you are never gonna multiply vectors because there is no such thing. But still, I think its a bad notation. I personally prefer making a small circle instead of a dot like this: $\vec{A}\circ\vec{B}$.

20. Sep 19, 2006

### CRGreathouse

Oh good, that way you can cnfuse it with composition instead. Yeah, they aren't functions you can compose... but they aren't numbers yo ucan multiply, either.