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Magenta
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I cannot remember if infinity is an upper bound for a subset of R?
I think so, but I want to be sure before I use it in a proof.
I think so, but I want to be sure before I use it in a proof.
Magenta said:I cannot remember if infinity is an upper bound for a subset of R?
I think so, but I want to be sure before I use it in a proof.
When we say that a set is bounded by infinity, we mean that the elements in the set do not have a specific upper limit or maximum value. In other words, the set has an infinite number of elements that are continuously increasing without ever reaching a limit.
No, a set cannot be both bounded and unbounded by infinity. A set is either bounded, meaning it has a specific upper and lower limit, or unbounded, meaning it has no specific limits. If a set is unbounded, it cannot be bounded by infinity because there is no limit to the elements in the set.
To determine if a set is bounded by infinity, we can look at the elements in the set and see if they have a specific upper limit or maximum value. If the elements continue to increase without ever reaching a limit, then the set is bounded by infinity.
No, not all infinite sets are bounded by infinity. Some infinite sets have specific limits, such as the set of all even numbers. This set has an infinite number of elements, but they are all bounded by the limit of 2.
The concept of boundedness by infinity is closely related to the concept of real numbers. Real numbers are continuous and have no gaps, meaning they can be infinitely divided without ever reaching an end. This is similar to how a set bounded by infinity has an infinite number of elements that continue to increase without ever reaching a limit.