which is the most reasonable estimate for the Depth of a lake... 6 millimeter 6 centimeters or 6 meters??? explain

Alex says that there is no numbers between 1/3 and 1/4 . Why might he think that and what would you tell him? Is there a number

Thepotemich [5.8K]

Answer:

Why might he think that and what would you tell him?

He thought perhaps that numbers were formed by rational numbers of the form $\frac{1}{x}$ , where $x\in \mathbb{N}$ . I would tell him that there are rational numbers $\frac{y}{z}$ , such that $\frac{1}{x}\le \frac{y}{z} \le \frac{1}{x+1}$ , where $x$ , $y$ , $z \in \mathbb{N}$ .

Is there a number that falls between these?

$\frac{7}{24}$ is a rational number between $\frac{1}{3}$ and $\frac{1}{4}$ .

Step-by-step explanation:

Why might he think that and what would you tell him?

He thought perhaps that numbers were formed by rational numbers of the form $\frac{1}{x}$ , where $x\in \mathbb{N}$ . I would tell him that there are rational numbers $\frac{y}{z}$ , such that $\frac{1}{x}\le \frac{y}{z} \le \frac{1}{x+1}$ , where $x$ , $y$ , $z \in \mathbb{N}$ .

Is there a number that falls between these?

Indeed, the average number of $\frac{1}{3}$ and $\frac{1}{4}$ , for instance. That is:

$\frac{y}{z} = \frac{\frac{1}{3}+\frac{1}{4} }{2}$