What are yses of finding upper and lower bound of the cylinder and example?
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A set with upper bounds and its least upper
bound.
In mathematics, especially in order theory ,
an upper bound of a subset S of some
partially ordered set ( K , ≤) is an element of
K which is greater than or equal to every
element of S .[1] The term lower bound is
defined dually as an element of K which is
less than or equal to every element of S . A
set with an upper bound is said to be
bounded from above by that bound, a set
with a lower bound is said to be bounded
from below by that bound. The terms
bounded above ( bounded below ) are also
used in the mathematical literature for sets
that have upper (respectively lower)
bounds.
Examples
For example, 5 is a lower bound for the set
{ 5, 8, 42, 34, 13934 }; so is 4; but 6 is not.
Another example: for the set { 42 }, the
number 42 is both an upper bound and a
lower bound; all other real numbers are
either an upper bound or a lower bound for
that set.
Every subset of the natural numbers has a
lower bound, since the natural numbers
have a least element (0, or 1 depending on
the exact definition of natural numbers). An
infinite subset of the natural numbers
cannot be bounded from above. An infinite
subset of the integers may be bounded
from below or bounded from above, but not
both. An infinite subset of the rational
numbers may or may not be bounded from
below and may or may not be bounded
from above.
Every finite subset of a non-empty totally
ordered set has both upper and lower
bounds.
A set with upper bounds and its least upper
bound.
In mathematics, especially in order theory ,
an upper bound of a subset S of some
partially ordered set ( K , ≤) is an element of
K which is greater than or equal to every
element of S .[1] The term lower bound is
defined dually as an element of K which is
less than or equal to every element of S . A
set with an upper bound is said to be
bounded from above by that bound, a set
with a lower bound is said to be bounded
from below by that bound. The terms
bounded above ( bounded below ) are also
used in the mathematical literature for sets
that have upper (respectively lower)
bounds.
Examples
For example, 5 is a lower bound for the set
{ 5, 8, 42, 34, 13934 }; so is 4; but 6 is not.
Another example: for the set { 42 }, the
number 42 is both an upper bound and a
lower bound; all other real numbers are
either an upper bound or a lower bound for
that set.
Every subset of the natural numbers has a
lower bound, since the natural numbers
have a least element (0, or 1 depending on
the exact definition of natural numbers). An
infinite subset of the natural numbers
cannot be bounded from above. An infinite
subset of the integers may be bounded
from below or bounded from above, but not
both. An infinite subset of the rational
numbers may or may not be bounded from
below and may or may not be bounded
from above.
Every finite subset of a non-empty totally
ordered set has both upper and lower
bounds.
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