╔(σ_σ)╝ said:Well you simply want to define X+Y such that some points are deleted.:-)
╔(σ_σ)╝ said:Well define one point in X to be negative the other point in Y.
robertdeniro said:i still haven't figure this out yet...but i was wondering if the solution has a "hole" in an interval?
and I am still confused about the "deleting" suggestion. since a negative and a positive would only produce zero and not remove the element from the set. in essence, you can only stretch and shift an interval.
robertdeniro said:i think if X=the integers and Y=sqrt(2) * the integers then it would work.
i still can't think of an example where points are deleted.
A counter example in real analysis is a specific example that disproves a given statement or theorem. It is used to show that a general statement is not always true by providing a specific case in which it does not hold.
To come up with a counter example, you first need to clearly understand the statement or theorem you are trying to disprove. Then, you can use your knowledge of mathematical concepts and techniques to construct a specific example that goes against the given statement.
No, not all counter examples are valid in real analysis. A counter example must be well-defined and follow the rules and principles of mathematics. If a counter example is found to be invalid, it means that the original statement or theorem holds true.
No, a counter example is used to disprove a statement or theorem. It cannot be used to prove a statement, as a single example does not necessarily prove a general statement to be true.
Counter examples are important in real analysis because they help to identify the limitations of a statement or theorem. They also encourage critical thinking and can lead to the discovery of new mathematical concepts and theories.