$\reals^2$ and $\mathbb{C}$, as real vector spaces

Example · Undergraduate

Terms

Term	This example	Why
isomorphic	✓
identified	✓	$\reals^2$ and $\mathbb{C}$ are often identified through the linear bijection $(a, b) \mapsto a + b i$.
equivalent	✓	$\reals^2$ and $\mathbb{C}$ are equivalent as real vector spaces, because they are isomorphic.
equal	✗	$\reals^2$ and $\mathbb{C}$ are not equal, because their elements are different objects.

Distinctions using this example

• Types of sameness

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