What does [-1,0]x{0} mean in box notation?

[javi438]

Homework Statement

can someone please explan what the line segment [-1,0]x{0} means? i don't understand the notation. if someone could explain it to me it would help me a lot!

thanks!

Homework Equations

The Attempt at a Solution

 

[Dick]

It means the set of all ordered pairs (x,0) where -1<=x<=0.

 

[javi438]

so what would [1,0]x[1,0] mean?

the set of (x,y) such that 1<=x<=0 and 1<=y<=0?

does the x in between the two [1,0]'s mean anything?

 

[Dick]

Sure. If you interpret (x,y) as a point in the plane that's a square. The 'x' is called the cartesian product. AxB is the set of all (x,y) such that x is in A and y is in B. (BTW you usually want to write the unit interval as [0,1], not [1,0]).

 

[javi438]

how about in this case?

S = {(x,y) : x and y are rational numbers in [0,1]}
the closure and boundary of S = [0,1]x[0,1]

what would it mean in this case, word for word?

 

[Dick]

You know what the sets mean, right? It says that the closure and boundary of the set of all rational points in the filled unit square are equal to ALL points in the filled unit square. (By filled I mean it includes the interior of the square).