Is it by definition that i^2=-1

[matt grime]

It appears you're writing as a platonist, whereas I am viewing it as a formalist.

And I still don't see you justifiying why:

his famous formula could only be derived if he allowed srt(-1)*srt(-1)=-1

You can let things behave differently at different times, you know, depending on circumstance. Now, of course, we don't, for sqrt(-1), but as I say that is a modern view on functions. Perhaps he manipulated things in whichever way he saw fit at the time, such as some people do with the axiom of choice or constructibility.

 

[arildno]

I would think that whatever complex maths Euler was doing, it was internally consistent.
That, however, does not mean he was doing complex maths as we choose to do it.

 

[pivoxa15]

It appears you're writing as a platonist, whereas I am viewing it as a formalist.

And I still don't see you justifiying why:

his famous formula could only be derived if he allowed srt(-1)*srt(-1)=-1

I am probably writing more as a naive mathematician but definitely not a platonist.

In this website http://en.wikipedia.org/wiki/Euler's_formula it seems that only if i^2=srt(-1)*srt(-1)=-1=-1 can Euler formula be derived. Are you suggesting there is a way to derive this formula by allowing i^2 to equal something else?

You can let things behave differently at different times, you know, depending on circumstance. Now, of course, we don't, for sqrt(-1), but as I say that is a modern view on functions. Perhaps he manipulated things in whichever way he saw fit at the time, such as some people do with the axiom of choice or constructibility.

That is interesting. It just shows how much more maths is a product of the human mind rather than some objective, indepedent reality.

 

[matt grime]

Are you suggesting there is a way to derive this formula by allowing i^2 to equal something else?

I am saying that there is quite possibly a method (for Euler) to demonstrate that

exp(ipi)+1=0

without ever stating what sqrt(-1)*sqrt(-1) is or isn't.