4Fun:Worst/Best Notations in Mathematics

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In summary, participants of the conversation discussed notations and symbols in mathematics that they find annoying or interesting. Some of the examples mentioned were the use of p and q as summation indices, the confusion between sin^2 and sin of sin, the factorial notation causing misunderstanding, and the use of ln for natural logarithm. They also mentioned helpful notations like the use of bars in z's to differentiate from 2's, the Christoffel Symbol, Poisson bracket, and Commutator. Some participants also expressed dislike for using bold letters to denote vectors and unit vectors and suggested using arrows instead. Overall, they agreed that there should be a better notation for iterated functions and unit vectors.
  • #71
chroot said:
As CRGreathouse mentioned, the use of the word "function" is not appropriate for a relation which is multi-valued.
Why is that?
 
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  • #72
Swapnil said:
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.
 
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  • #73
CRGreathouse said:
Division on the integers is an example, since division by 0 is undefined.

And by "integers", I mean "reals".
 
  • #74
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).
 
  • #75
The number 3 is pretty confusing to be honest
 
  • #76
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 [tex]\frac{d}{dx}[/tex] operator. :biggrin:
 
  • #77
One more thing that I realized is that the function notation [tex]e^{(.)}[/tex] 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 [tex]\exp(.)[/tex] is a far better notation in the long run.
 

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