Bounded Below Real Sequence/Examples/Strictly Positive Integers

Example of Bounded Below Real Sequence

Let $\sequence {s_n}$ be the real sequence defined as:

$s_n = n$

That is:

$\sequence {s_n}$ is the sequence of strictly positive integers.

Then $\sequence {s_n}$ is bounded below.

Proof

All strictly positive integers are by definition greater than zero.

Hence $0$ is a lower bound of $\sequence {s_n}$.

Hence the result by definition of bounded below.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): bounded sequence
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): bounded sequence