Interesting observations. I'd like to write this up - I might later - I don't have time now - here's some material from Feynman ... Take successive square roo

Interesting observations. I'd like to write this up - I might later - I don't have time now - here's some material from Feynman ... Take successive square roots of 10. As you get further and further you spot a pattern, that when e is very small, 10^e ~ 1+c.e for some constant c. Now take 10^(i.e) where e is very small and i=sqrt(-1). Then 10^(i.e) ~ 1+c.i.e. Take repeated powers and you end up moving in a circle. Following that we end up with the formula e^(i.t) = cos(t)+i.sin(t) where t is a real angle. None of that works if you don't basically take the reals for granted. Or at least, it's very hard.