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Topic: Bijection Between Complex Numbers and Real Numbers
Replies: 59   Last Post: Feb 24, 2012 7:12 AM

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 David Yen Posts: 630 Registered: 3/1/11
Re: Bijection Between Complex Numbers and Real Numbers
Posted: Feb 22, 2012 10:25 AM

Good point! But, zero is probably not a normal number. Zero violates closure under division in all possible subsets of numbers that include it. Yet, closure is required for a magma.

If you must include zero in the usual sense, then the unary system (base 1) has to be used. I don't know how you can define real numbers in unary though.

The point is, it is really pointless to ask for an exact bijection between R and R^2. What do you need it for?

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