Rather easy problem involving set multiplication

[U.Renko]

Homework Statement

A = { 1, 1, 2, 5}
B = [1, 2]

find A x B

Homework Equations

not much

The Attempt at a Solution

well, the problem itself seems easy enough
The thing is, I'm not very sure what it means to multiply a set by an interval...

just need a little help with this detail

 

[Bacle]

But what's confusing is that the set {1,1,2,5} is the same as {1,2,5}, by basic set properties.

One way of understanding the product of a set by an interval is by considering a subset
of the product of 2 intervals, say , the interval [1,5], and [1,2] , then {1,2,5}x [1,2] will
just give you three discrete copies of the interval [1,2]. Or look at the square [0,1]x[0,1] , then {0,1}x[0,1] are just the bottom and the top of the square, respectively.

 

[SammyS]

You could express the result using set builder notation.

For example:

{1,3}×[0,1] = {(1,y)|0≤y≤1} ∪ {(3,y)|0≤y≤1}

= {(x,y)|x∊{1,3}, 0≤y≤1}

 

[U.Renko]

You could express the result using set builder notation.

For example:

{1,3}×[0,1] = {(1,y)|0≤y≤1} ∪ {(3,y)|0≤y≤1}

= {(x,y)|x∊{1,3}, 0≤y≤1}

The thing is, in the book I'm using, up to this exercise, Unions and the such were not defined yet.

also I'm not 100% sure that {1,1,2,5} = {1,2,5}
shouldn't one have cardinality 4 and the other cardinality 3 ?

might make some difference.

 

[SammyS]

List the elements in each set. {1,1,2,5} ; {1,2,5} .