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lolgarithms
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Does the field of "hypercomplex numbers" (*C; a+bi with a,b hyperreal numbers) satisfy the transfer principle? Are all of the arithmetical facts with complex numbers true with the hypercomplex numbers?
One might be able to construct a nonstandard complex analysis with the hypercomplex numbers, with identical results as as standard complex analysis, with the standard part function st(z) = st(Re(z)) + i st(Im(z)) used to define complex derivatives and integrals.
One might be able to construct a nonstandard complex analysis with the hypercomplex numbers, with identical results as as standard complex analysis, with the standard part function st(z) = st(Re(z)) + i st(Im(z)) used to define complex derivatives and integrals.
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