Richard Baker wrote: 
>  
>> The number of sets of infinite vectors with one scalar zero  
>> is also infinite, but a much bigger infinite  
>  
> Uh, the components of a vector aren't scalars because 
> they aren't unchanged by changes in coordinate system. 
 
I am using an heterodox definition of scalar. A scalar 
is anything that is not a vector, but is a part of 
a vector. 
 
> But that's why I was confused by Mark's message - 
> I translated "scalar of a vector" into 
> "inner product of vector with itself" and then it all 
> looked like nonsense. 
 
It looked like nonsense because you are too Cartesian. 
Maybe you should think in some Riemmanian space, where 
the theorem of Pythagoras is no longer valid. 
 
Alberto Monteiro 
 
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