Why ##a^0=1##?

[sophiecentaur]

I like this definition (on Wiki article).

There's quite a high level of sophistication about rational indices. Also even for all arithmetic with rational numbers; we tell kids about 'sharing' and division but even that is a matter of going through the motions and believing you got a right answer. As a lifetime Engineer, I'm used to a black box approach to Maths - as a tool and not a religion.

 

[Mike_bb]

For example, do you know the mechanics of deriving dy/dx for y=cos(x) and where the 'limit' is involved (plus some elementary trig identities).

Yes, I do. I studied full course of Math. But your example has another type of definition. Of course, if we are talking about derivatives we should use limit conception to define. "Derivative of a function" means that we "derive some function" and thus we use limit.

 

[Andrew Mason]

If $a^0\ne 1$ then $a^0\ne -e^{\pi i}$ and the beauty of mathematics would be gone.

AM

 

[sophiecentaur]

Yes, I do. I studied full course of Math. But your example has another type of definition. Of course, if we are talking about derivatives we should use limit conception to define. "Derivative of a function" means that we "derive some function" and thus we use limit.

Pure or applied Maths course? The Pure Maths guys look after the souls of Scientists and engineers etc. who use Maths for their work. Your terminology is a bit approximate and it's not getting us anywhere.

I'm afraid that, unless you are a 'good' pure mathematician, you need to trust their authority a bit blindly and follow the 'rules' really which have been derived carefully. You can't pick and choose between those rules to suit yourself. I gave up trying to do that.

 

[Mike_bb]

Pure or applied Maths course? The Pure Maths guys look after the souls of Scientists and engineers etc. who use Maths for their work. Your terminology is a bit approximate and it's not getting us anywhere.

Pure Maths.