notes
these are some more informal notes that I have made after having taken the rigorous Analysis course.
- \(c_{00}\) can be thought of as ‘finite vectors’. all \(\mathbb{R}^n\) tuples can be written as elements of \(c_{00}\) with infinitely many zeros after the $n$th term.
- \(c_0\) are all sequences that converge to zero. thus they will include all those in \(c_{00}\) and more.
- \(\ell^2\) are the vectors that fade fast enough for their energy 𐃏 to stay finite
- \(\ell^\infty\) are the infinite vectors that never blow up – their entries are bounded.
\[c_{00} \subset c_0 \subset l^\infty \]