# Is there a way to make a set of all real numbers within a range? [closed]

Is there a way to create a set of all real numbers within a range? For example, the range between 1300 and 1500, including 1500 in normal distribution. Thank you very much.

My problem exactly:

• $A$ – The probability of rainfall/year being less than or equal to 1500 is $P[A]=0.17$

• $B$ – The probability of rainfall/year being between 1300 and 1700 (including 1700) is $P[B]= 0.33$

• $C$ – The probability of rainfall/year being less than, or equal to 1700 is $P[C]= 0.39$

What's the probability of P[A Intersection B]?

By hand, I solved this by defining the respective sets and making operations between them and from that, computing probabilities.

• Mathematica does not have a general "set type", so technically it is not possible to create any kind of set. But very likely it is possible to solve the problem you have, you just need to state the problem clearly. Can you explain what are you trying to do? – Szabolcs Nov 6 '15 at 9:50
• I want to define three sets like that, assign probabilities to them and then make operations with them, for example P[AUB], where A is the above mentioned set and B is the set for all reals lower or equal to 1700. – AlexV Nov 6 '15 at 9:53
• Yes, and all I found and tried was using Lists, but that's only for a specific n amount of numbers with a specific step, for example List[0,1500] creates a set of all integers between 0 and 1500 – AlexV Nov 6 '15 at 9:57
• What do you mean by "assign probabilities to a set"? You can define distributions over various intervals. Take a look at ProbabilityDistribution and the many other built-in distributions: reference.wolfram.com/language/guide/… reference.wolfram.com/language/guide/… I still don't understand your question though. It is best if you give a concrete example: "this is my input, this is the operation I want to do, this is the output I expect". – Szabolcs Nov 6 '15 at 10:01
• The sets represent events, each of these events has a certain probability of occurring. There is the event that the rainfall per year is less than, or equal to 1500 and its probability is 0.17. That's my example exactly. – AlexV Nov 6 '15 at 10:08