- #1
Seacow1988
- 9
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If A, B are nonempty subsets of R and A is a subset of B, how can you prove that: if A is unbounded, B is unbounded?
To prove unboundedness of B if A is unbounded, you need to show that for any positive number M, there exists a number x in B such that x is greater than M. This means that B has no upper bound and is therefore unbounded.
In order to prove unboundedness of B, you must first know that A is unbounded. This is because if A is bounded, then B cannot be unbounded.
Sure, let's say that A is the set of all positive integers and B is the set of all even integers. Since A is unbounded, there is no limit to how large the positive integers can be. This means that B, which is a subset of A, is also unbounded.
No, it is not possible for B to be unbounded if A is bounded. This is because B is a subset of A, so it cannot have a larger limit than A. If A is bounded, then B must also be bounded.
If you are able to prove unboundedness of B if A is unbounded, then it means that B has no upper bound and can potentially grow infinitely. This can be useful in mathematical proofs and can have real-world applications in fields such as economics and physics.