Itqualityassurance
- Can an upper bound be infinity?
- How do you show something is an upper bound?
- Can limit supremum be infinity?
- Does infinity have a bound?
Can an upper bound be infinity?
The exact definition of infinity is contextual, but in general ∞ represents something increasing without bound (which means there is no upper bound for the function), and −∞ represents something decreasing without bound (which means there is no lower bound for the function).
How do you show something is an upper bound?
Consider S a set of real numbers. S is called bounded above if there is a number M so that any x ∈ S is less than, or equal to, M: x ≤ M. The number M is called an upper bound for the set S. Note that if M is an upper bound for S then any bigger number is also an upper bound.
Can limit supremum be infinity?
lim sup and lim inf always exist (possibly infinite) for any sequence of real numbers.
Does infinity have a bound?
infinity, the concept of something that is unlimited, endless, without bound. The common symbol for infinity, ∞, was invented by the English mathematician John Wallis in 1655.
