Question

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

Answer 1

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

`S = \{0, 1\}`

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 < (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`