4 ms·
Not a mathematician so correct away: I think the initial confusion stemmed from not pinning down the domain of x and y. When he says “I don’t see the complex
by elteto 6y ago
Not a mathematician so correct away:
I think the initial confusion stemmed from not pinning down the domain of x and y.
When he says “I don’t see the complex points” in the xy graph that is because they aren’t there: the xy graph is in R^2 and x^2 + 1 = y has no solution in the reals for y = 0.
But if you imagine, as he did, an extra dimension attached at each point then that is now a complex space, is it not?
- potiuper 6y agoThe domains of x and y both appear defined as the real numbers. But, the reals do not have a root for every non-constant polynomial defined in terms of x or y as the real numbers are an not algebraically closed field. The proposed concept attaches two extra (complex) dimensions to each two dimensional real point. This is close to visualizing R^4 by attaching an R^2 to each point of R^2, so in some sense the tangent bundle of R^2.