Question

Write the set of non-negative integers in the inequality 2x < 4.

Answer 1

Answer:

The set $S$ of non-negative integers in the inequality $2x < 4$ is

$S = \{0, 1\}$

Step-by-step explanation:

The non-negative integers are given as $\mathbb{Z}_{\ge 0} = \{ 0, 1, 2, \ldots \}$

For the inequality $2x < 4$, we have

$2x < 4 \implies x < \dfrac{4}{2} \implies x < 2$

Therefore,

$x\in \mathbb{R}:x\in(\infty, 2)$

Note: 2 is not included

The integers are

$\ldots -2, -1, 0, 1$

And the non-negative integers are

$0, 1$