This is Real.pic.twitter.com/E5JQYz39dp
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I saw this on a turkish blog and in this blog somebody says i^i is not real since the set of Complex numbers is C={(a,b): a,b real numbers}. He said that the only difference with R^2 is operations. Product is different bu him. I found this explanations are bullshit.Wt do u think?
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I think C={z: z=a+ib , i^2=-1} it has no such defn. It is just similarity. It is isomorph to R^2.
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I'm not so sure if the two spaces are isomorphic. They "look alike".. but there are theorems that are true in C that just aren't true in R^2.. e.g. a function that is differentiable is infinitely differentiable.
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