- #1

- 222

- 17

"or every x>0, all the elements of closed set [a+x,b-x] are elements of A"?

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- #1

- 222

- 17

"or every x>0, all the elements of closed set [a+x,b-x] are elements of A"?

- #2

Science Advisor

- 1,082

- 85

##\forall x>0##, ##[a+x, b-x] \subset A##,

which is a true statement.

But

##\forall x>0##, ##[a+x, b-x] \subset [a,b]##

is also a true statement, so you can't use it to define A.

- #3

- 222

- 17

Yes you are right...It just becomes a subset. But is there any way to describe it?

- #4

Science Advisor

- 1,082

- 85

- #5

- 222

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