Re: More complex numbers than reals?

On 2024-07-08, Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:

Are there "more" complex numbers than reals? It seems so, every real has
its y, or imaginary, component set to zero. Therefore for each real
there is an infinity of infinite embedding's for it wrt any real with a
non-zero y axis? Fair enough, or really dumb? A little stupid? What do
you think?

The argument is not that simple. If we restrict to just integer complex
numbers like 4 + 5i, then no; there aren't more of these than integers.
Yet the same argument about axes and embeddings could be wrongly applied.

Integer complex numbers are countable: you can start at 0, and then go
in a spiral fashion:  1, 1 + i, i, -1 + i -1, ...  thus they can be put
into correspondendce with the natural numbers.

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