- #1

- 214

- 0

## Homework Statement

A textbook of mine asserts that ℝ is a subset of ℂ. The motivation for this is drawn by defining complex addition and multiplication and then showing that these operations on complex numbers of the form (x,0), with x an element of ℝ, are isomorphic to the field ℝ witih addition and multipication as ordinarily defined there. This may be nitpicky, but in order to state that ℝ is a subset of ℂ, isn't it necessary to have that 0i = 0, so that x + 0i = x + 0 = x, which is already assumed to be in ℝ? This isn't explicitly mentioned anywhere though (since i is not a real number and hence we can't automatically deduce that 0i = 0 from the [real] field axioms).