Let f(z) is be complex function and u(x,y) & v(x,y) be real functions.
f(z) is said to be holomorphic if u,v satisfy the Cauchy-Riemann equationspic.twitter.com/C0MPdaAg5w
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Hmmm. So, in one variable, if it’s holomorphic, it’s analytic across the entire variable... I’ll buy that, but I keep thinking of possible singular points, but maybe those are precluded by CR. I have to think about this, but, maybe I wasn’t wrong all these years 
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