functions | e^(ix)

Problem

Describe, in words, each of the following sets:

$x < 0$
$x \leq 0$
$a < x \leq b$
$- \infty < x < 5$ , $x = 7$
$-3 < x < -2$ , $x > 0$
$\sqrt{2} < x < \pi$
$2 \pi \leq x < 3 \pi$

Solution

$x < 0$ is a set of all negative numbers.

$x \leq 0$ is the set of all numbers that are less than or equal to 0. In $\mathbb{R}$ it has an infinite number of elements.

$a < x < \leq b$ is the set of all real numbers that are greater than a and less than or equal to b, depending on what a and b are. This implies that $a < b$ .

$- \infty < x < 5$ , $x = 7$ is the set of all real number lower than 5 and the number 7.

$-3 < x < -2$ , $x > 0$ is the set of all positive real number and any number between -3 and -2, but not including -3 and -2.

$\sqrt{2} < x < \pi$ is the set of all real number greater than $\sqrt{2}$ (~1.414) and $\pi$ (~3.14159) but not including $\sqrt{2}$ and not including $\pi$ .

e^(ix)

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