- #1

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## Main Question or Discussion Point

Prove that the set of complex numbers has the same cardinality as the reals.

What I did was say that a + bi can be written as (a, b) where a, b belong to real. Which essentially means i have to create a bijection between (a, b) and z (where z belongs to real).

Suppose:

a = 0.a1a2a3a4a5...

b = 0.b1b2b3b4b5...

Then,

z = 0.a1b1a2b2a3b3....

Is there anything wrong with that?

What I did was say that a + bi can be written as (a, b) where a, b belong to real. Which essentially means i have to create a bijection between (a, b) and z (where z belongs to real).

Suppose:

a = 0.a1a2a3a4a5...

b = 0.b1b2b3b4b5...

Then,

z = 0.a1b1a2b2a3b3....

Is there anything wrong with that?