Have you found ?
I am considering the sequences of continuous functions defined by:
How do I show that is a cauchy-sequence in the normed vector space and how do I examine if the mentioned normed vector-space is a banach space (i know that every finite dimensional normed vector space is a banach space).
is the normed vector space of continuous real-valued functions defined in the closed interval .
Stupid question: How did you get ?
Since I have shown that:
the norm you are asking for becomes:
I would say that this expression goes to 0 as and tend towards infinity.
Per definition i know that for a sequence to a be a cauchy-sequence it must hold that:
Could I conclude that since the expression above tends towards 0 (which is smaller than ) for going towards infinity, that is a cauchy-sequence?