Correct Notation for Intersections of Real Numbers Sets

[danago]

Lets say i have two sets of numbers (dealing with real numbers only):

$$\{ x \in R |x \ge 0\}$$
$$\{ x \in R |3 \ge x\}$$

And i want to show what the common values in the two sets are. Would my notation be correct if i wrote:

$$\{ x \in R |x \ge 0\} \cap \{ x \in R |3 \ge x\} = \{ x \in R |3 \ge x \ge 0\}$$


Thanks in advance,
Dan.

 

[cristo]

One would normally write the double inequality in increasing size: $\{x\in\mathbb{R}:0\leq x\leq3\}$

 

[HallsofIvy]

That is not incorrect but I suspect those who are used to a number line that goes from left to right would find it momentarily confusing!

Most people would find it easier to read
$$\{ x \in R |0 \le x \le 3\}$$

 

[danago]

Ok that's fair enough, easy enough to change

But besides that, everything else ok?

Thanks for the replies.