4Fun:Worst/Best Notations in Mathematics

[FrogPad]

just keep asking,
'huh?"

thats what you are paying for.

hehe.
true that

 

[cliowa]

There's another incredibly annoying thing some mathematicians do (one can see this very often in books):
They take two different things, but give them the exactly same notation (because the word begins with the same letter or because traditionally it always is n, so the author can't brake with tradition), stating that it will be clear in the context which one is meant. I hate that!

 

[mtanti]

Once I was explaining factorials to a friend in a chat room and I said 'do you know what is 3x2x1?' I said '3!'.

The reply was 'why are you shouting?'

It also gets pretty confusing when you put the factorial in a question: 'what is 3!?'

You end up having to use brackets around the number (3!)

 

[Swapnil]

Personally, I don't like the \sqrt sign, because it makes it seem that exponents are something magical. Think of the things that might go through a middle school student's mind when he is asked to take raise \sqrt 3 to the power of 3! ( BTW, I mean just the number 3, not 3 factorial!).

Plus, the squareroot sign is also long and ugly.

 

[Swapnil]

Another fact that I dislike is the use of the term "function." Sometimes, a function simply means a correspondence (a rule by which we assign each object in a set some other object(s) in some other set).

Other times it means a special TYPE of correspondence (the one which takes an object in a set and maps it to a single UNIQUE object in another set).

 

[CRGreathouse]

Another fact that I dislike is the use of the term "function." Sometimes, a function simply means a correspondence (a rule by which we assign each object in a set some other object(s) in some other set).

Other times it means a special TYPE of correspondence (the one which takes an object in a set and maps it to a single UNIQUE object in another set).

I never use it in that first sense. I use the term "relation" instead.

 

[chroot]

As CRGreathouse mentioned, the use of the word "function" is not appropriate for a relation which is multi-valued. If your teachers are using the term this way, I pity them.

- Warren

 

[0rthodontist]

Another fact that I dislike is the use of the term "function." Sometimes, a function simply means a correspondence (a rule by which we assign each object in a set some other object(s) in some other set).

Other times it means a special TYPE of correspondence (the one which takes an object in a set and maps it to a single UNIQUE object in another set).

Are you talking about the use of "function" to denote partial functions?

 

[Swapnil]

What do you mean by "partial functions"?

 

[CRGreathouse]

What do you mean by "partial functions"?

Let f:A\rightarrow B be a function. Then f':A'\rightarrow B, where A\subsetneq A' and f' is equal to f on A and undefined otherwise, is a partial function from A' to B.

Essentially, it's a function that isn't defined everywhere. Division on the integers is an example, since division by 0 is undefined.

 

[Swapnil]

As CRGreathouse mentioned, the use of the word "function" is not appropriate for a relation which is multi-valued.

Why is that?

 

[arildno]

Why is that?

Because a "function" is defined to be SINGLE-valued.
It is a fact of life.

Also note that what we might call a "multi-valued" function, can always be considered as a single-valued function from the given domain and having as its co-domain the POWER SET of of the set containing the various function values.

 

[CRGreathouse]

Division on the integers is an example, since division by 0 is undefined.

And by "integers", I mean "reals".

 

[Gelsamel Epsilon]

A person in my calculus class got upset and stormed out of class because she kept confusing imaginary numbers with vector measurements (use of i in both).

 

[Office_Shredder]

The number 3 is pretty confusing to be honest

 

[Swapnil]

I hate the prime notation for derivatives because, in physics, people often use variables like x and x' and this can be confusing sometimes. Although, I have to say that when used unambigiously, the prime notation for derivatives is pretty useful and often takes away the scary \frac{d}{dx} operator.

 

[Swapnil]

One more thing that I realized is that the function notation e^{(.)} is very limited. I mean that when the argument in the exponent gets complicated (which happens often I think), it becomes really hard to distingush what's an exponent and what's not. I would say that \exp(.) is a far better notation in the long run.