Prove that

*Proof.* Let

Then,

This holds if and only if

From the usual limit this is true if and only if

This is if and only if

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#
Stumbling Robot

A Fraction of a Dot
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Prove a property of limits of vector valued functions

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### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

Prove that

*Proof.* Let

Then,

This holds if and only if

From the usual limit this is true if and only if

This is if and only if

The problem statement is for the norm of the vector, not its absolute value. However, it’s just another iff that cab be easily proven when going to the limit definition.