Real Limit Algebra
Why
Consider two convergent sequences. What if we add them termwise? Or multiply?
Main results
Let $(x_n)_{n \in \N }$ and $(y_n)_{n \in
\N }$ be two limits with $x_0$ and $y_0$ in
$\R $.
Then the sequence $(s_n)$ defined by $s_n =
x_n + y_n$ converges to the limit $x_0+ y_0$
and the sequence $m_n = x_ny_n$ converges to
the limit $x_0y_0$.1
In particular for $a \in \R $, the sequence $(c_n)$ defined by $c_n = ax_n$ converges to the limit $ax_0$.
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