Official TSR Mathematical Society

Hmm, but are there numbers outside of the complex set? (I should know but I, err, don't.)

Yes and no. There are other number systems: Quaternions, Octonians... but that's slightly different

You would really need to start by telling me what you mean by "numbers"

Quaternions was the system I was thinking about, but neglected to mention them as I don't really know what they're about. Come to think of it, I'm not sure I'd define a "number".

$\mathbb{H}$? (I have no experience of Quaternions).

You do maths while out for a meal?

This is a hard problem.

Solve

$x+2=3$

My method

$x+2=3$

$(x+2)\times0= 3\times 0$

$x\times 0 + 2 \times 0= 0$

$x\times 0 = 0$

$x=\frac{0}{0}$

$x=0^0$

$x=1$ using the fact that $a^0=1$ for all a.

Check
$1+2=3=3$

He's picking up my bad (?) habits.

I don't know about bad, I was thinking more unusual. "I'll have the soup of the day, but will you give me a minute to solve this cubic first?" I just can't imagine it.

"Anything else with your meal madam, salt and vinegar perhaps?"
"No thank you, just a protractor"

No no, definitely can't imagine it.