I'm not sure where to start on this whole set and subset topic.
represent the following set using set-builder notation:
{0,2,4,...,12}
My teacher told me that three dots ... meant an infinate set, but looking at
the problem more i would think the answer would be {0,2,4,6,8,10,12}
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No, three dots (called an "ellipsis") only indicates an infinite set if it
doesn't have a stopping number after it.
The set {0,2,4,...} is an infinite set because there is no stopping number
written after the three dots, so it goes on and on forever.
However, your set {0,2,4,...,12} does have a stopping number, namely 12,
so you are right that it means the same thing as {0,2,4,6,8,10,12}.
What you are supposed to do is write it as:
"the set of all numbers representable by the variable x such that
x is greater than -1 and less than 13 and x is an even integer"
only abbreviated this way:
{x | -1 < x < 13, x an even integer}
That's what is meant by "set-builder" notation.
Edwin