English: # A bounded sequence ${\displaystyle (x_{n})}$ on the real number line with one of its lower bound ${\displaystyle s}$ and one of its upper bound ${\displaystyle S}$.

1. We take the first interval ${\displaystyle I_{1}=[s,S]}$.
2. Now we split the interval ${\displaystyle I_{1}}$ into twi equally sized subintervals.
3. We take this subinterval for ${\displaystyle I_{2}}$, which contains infinitely many members of ${\displaystyle (x_{n})}$
4. Then we split ${\displaystyle I_{2}}$ again into two equally sized subintervals.
5. We take this subinterval ${\displaystyle I_{3}}$ which contains infinitely many members of ${\displaystyle (x_{n})}$
6. With continuing this process we get nested intervals. The point being in all those intervals is an accumulation point of ${\displaystyle (x_{n})}$.