Questions About Intervals in Calculus for 14 Year Olds

[Ygmaince241]

Ok, I'm very new to calculus, and was stuck on the very basics of it. I'm only 14, but am extremely interested in math and science. I was inspired to study calculus when reading a book named, "Five Equations that changed the World", by Michael Guillen. Now I was doing some problems involving intervals. The book tells me to sketch the sets. The one problem is (-3,2] U (1, 7]. What exactly does the U stand for? The answer they gave for the example was, (1,2]. I know "(" stands for an open end, and "[" stands for a closed end. How do these apply to the sets. I couldn't see how they got the answer. Please help.

 

[Muzza]

\cup is union.

But are you sure the problem didn't ask for the intersection, (-3, 2] \cap (1, 7], of the intervals...?

 

[AKG]

Ok, I'm very new to calculus, and was stuck on the very basics of it. I'm only 14, but am extremely interested in math and science. I was inspired to study calculus when reading a book named, "Five Equations that changed the World", by Michael Guillen. Now I was doing some problems involving intervals. The book tells me to sketch the sets. The one problem is (-3,2] U (1, 7]. What exactly does the U stand for? The answer they gave for the example was, (1,2]. I know "(" stands for an open end, and "[" stands for a closed end. How do these apply to the sets. I couldn't see how they got the answer. Please help.

Like Muzza said, that answer only makes sense if they were asking for the intersection of the two intervals, not the union. I don't exactly understand your problem. Do you understand what "open end", "closed end", "intersection", and "union" mean?

 

[Ygmaince241]

Omg, yes. The problem was asking for an intersection. Sorry for not being specific enough.

 

[Nexus[Free-DC]]

Hey there Ygmaince241.

With the union and intersection symbols it's sometimes a bit hard to remember which is which. I always think of it this way: \cupnion and i\captersection.

 

[napoleonmax]

A good way to solve for unions and intersections (if you're really stuck) is to draw a number line with both sets on it. Union is all the numbers in both sets while intersection is the common numbers.
ex.
_____-1_____0_____1___
<~~~~~~~o (-infinity, 0) 0=open, •=closed
•~~~~~~~~~~> [-1, infinity)
Looking at this, you can clearly see that the intersection is [-1, 0) and the union is
(-infinity, infinity)