What would be necessary to redefine notations in maths?

I thought of this question after reading "Fezza"'s post on tan^(-1) Vs arctan

First of all I'm going to say what I have to say. I absolutely hate the notation of sin^2(x)=sin(x)sin(x).

To me it makes absolutely no sense why we don't write it as sin(x)^2 and define sin^2(x) as sin(sin(x)). Yes I know that's not as commonly used but being consistent is kind of the whole point of what maths is... So why not keep up with that in our notations?

I believe this would be a better notation due to how we use functions ( e.g.: f^(-1)(x) and f^2(x)=f(f(x)) )

So swiftly moving on from that rant. My question: what would we have to do to be able to redefine and standardise this? (or other mathematical notations such as logs etc.)

I understand it would be a very difficult thing to do but has it ever been done before and how could we do it?

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Comments (4)

Woogle

I had this same thought too once. But it is important to differentiate f^2(x) and f(x)^2.

This is not just notation.

It is not always true that that f^2(x)=f(x)f(x) as functions. As expressions yes, but not as functions.

Take sqrt(x), and x as an example. g(x)=x is defined on all real numbers while f(x)=sqrt(x) is not and neither is f^2(x). We would need to restrict the domain of g to make it the same as f.

Domain and range are important, that's why we go over it before function operations.

And this is especially important for trig functions since they need to have a restricted domain if we want to define arcsin and arccos.

0 Reply 10/04/19

Bearrito

I've seen textbooks use f^2 instead of f•f, where • is composition of mappings. This only demonstrates that one could use whatever notation wanted as long as the reader is informed. However, change of notation must be used sparingly in order to not bewilder or confuse the reader. I suggest using no more than 2 nonconventional notations at once.

0 Reply 10/04/19