# Search results

1. ### Henstock Integral Help

Homework Statement Prove \int\int_{[-1,1]×[-1,1]}f(x,y)dA is not Henstock Integrable. Homework Equations f(x,y) = \frac{xy}{(x^{2}+y^{2})^{2}} f(x,y) = 0 if x^{2}+y^{2}=0 on the region [-1,1]×[-1,1] The Attempt at a Solution The only hints given is that we will not be able to solve...
2. ### Intersection of a sequence of intervals equals a point

Intersection of a sequence of intervals equals a point (Analysis) Homework Statement Let A_{n} = [a_{n}, b_{n}] be a sequence of intervals s.t. A_{n}>A_{n+1} and |b_{n}-a_{n}|\rightarrow0. Then \cap^{∞}_{n=1}A_{n}={p} for some p\inR. Homework Equations Monotonic Convergent Theorem If...
3. ### Sup(A) less than or equal to sup(B)

Homework Statement Given A and B are sets of numbers, A \neq \left\{ \right\} , B is bounded above, and A \subseteq B . Explain why sup(A) and sup(B) exist and why sup(A) \leq sup(B). Homework Equations \exists r \in \mathbb R \: : \: r \geq a \: \forall a \in A \exists r \in \mathbb R...
4. ### Prove is countable

Homework Statement Prove that \mathbb Z^{+} X \: \mathbb Z^{+} X \: \mathbb Z^{+} is countable, where X is the Cartesian product. Homework Equations The Attempt at a Solution I'm lost as to where to start proving this.
5. ### Prove onto

Homework Statement Prove that if f: X \rightarrow Y is onto, then f(f^{-1}(B))=B \forall B \in Y Homework Equations The Attempt at a Solution
6. ### Prove inf(A)=0 *Practice*

Homework Statement Suppose A={\frac{1}{1},\frac{1}{2},....}={\frac{1}{n}|n\in{Z^+}} Homework Equations The Attempt at a Solution Could you take the limit of \frac{1}{n} as \infty to prove this, or would I go about it a different route?
7. ### How to start Z+ X Z+ -> Z+

Homework Statement Define f: Z+ X Z+ -> Z+ by f(a,b) = 2^(a-1)(2b-1) for all a,b in Z+ where Z+ is the set of all positive integers, and X is the Cartesian product Homework Equations The Attempt at a Solution If we assume (a,b) as ordered pairs and write them as follows: (1,1) (1,2)...