Let $(a_{n})_{n=1}^{\infty}$ be a \reftext{def:sequence-in-set-2026a}{sequence} of \reftext{def:real-numbers-c54-2026c}{real numbers}. Then the following hold.

\textbf{1. (Uniqueness of limits)} If $(a_{n})$ \reftext{def:limit-sequence-real-c54-2026a}{converges} to $A$ and also converges to $A'$, then $A=A'$.

\textbf{2. (Convergent sequences are bounded)} If $(a_{n})$ converges to some real number, then $(a_{n})$ is \reftext{def:bounded-sequence-real-c54-2026a}{bounded}.