user174558
Consider the following question on an elementary school math test paper.
The area of a right triangle with integral sides is 5. What is twice
its area?
Obviously, the answer is 10. But on closer inspection, there is no such right triangle.
Primarily, what can be done to avoid such mistak...
user174558
user174558
user174558
user174558
user174558
user174558
user174558
user174558
user174558
0
Consider the subspace of continuous, real-valued functions on $[0,1]$ that are Lipschitz. Is this subspace complete under the sup norm ($\Vert \cdot \Vert_{\infty} = \sup \{ |f(x)| : x\in S \}$)?
I would say yes, since all Lipschitz functions ($d_{Y}(f(x_{1}),f(x_{2}))\leq d_{X}(x_{1},x_{2})$, w...
In mathematics, a function f defined on some set X with real or complex values is called bounded, if the set of its values is bounded. In other words, there exists a real number M such that
for all x in X. A function that is not bounded is said to be unbounded.
Sometimes, if f(x) ≤ A for all x in X, then the function is said to be bounded above by A. On the other hand, if f(x) ≥ B for all x in X, then the function is said to be bounded below by B.
The concept should not be confused with that of a bounded operator.
An important special case is a bounded sequence, where X is taken to be the set...
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. 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.
== ExamplesEdit ==
5 is...
user174558
