Definition:Bounded Below Sequence/Real

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This page is about Bounded Below Real Sequence. For other uses, see Bounded Below.


Let $\sequence {x_n}$ be a real sequence.

Then $\sequence {x_n}$ is bounded below if and only if:

$\exists m \in \R: \forall i \in \N: m \le x_i$

Unbounded Below

$\sequence {x_n}$ is unbounded below if and only if there exists no $m$ in $\R$ such that:

$\forall i \in \N: m \le x_i$


Strictly Positive Integers

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.

Also see

  • Results about bounded below real sequences can be found here.