Equivalent Norms
# Definition
Let $(X, ||\cdot||)$ be a Normed Vector Subspace and let $Y \subset X$ be a Vector Subspace equipped with Norm $|||\cdot|||$. We say $||\cdot||$ is equivalent to $|||\cdot|||$ if they are both stronger than the other.
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Let $(X, ||\cdot||)$ be a Normed Vector Subspace and let $Y \subset X$ be a Vector Subspace equipped with Norm $|||\cdot|||$. We say $||\cdot||$ is equivalent to $|||\cdot|||$ if they are both stronger than the other.