This has been the question of the week for me and my maths teachers.

It started off when I was emptying the bins in the playground when I heard some some advanced higher maths students talking, I heard, "you know the easy stuff like differentiation...?"

"So you think that differentiation is easy do you?" I asked. "Differentiate x to the power of x."

They did what people usually do when they're first confronted with this; completely miss that this is a function rather than a function of a function. I pointed out their errors and they giggled at me.

Still that got me thinking, what is 0⁰ ? Do we want to say 1?

We agreed not to google this, or use our graphing calculators.So we were left to our own mathematics devices. 

I saw two fixed points but when I messed around I saw that I was being stupid. The only fixed point is 1, I thought that there was another around three-quarters, things got a wee bit odd there.

The graph is special play a wee bit for yourselves...