Intereting Posts

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Dr Math and his family question. How to solve without trial and error?
Real Analysis: Continuity of a Composition Function
Convergence in distribution (weak convergence)
a follow up question about modeling with exponential distributions
Mathematical problem induction: $\frac12\cdot \frac34\cdots\frac{2n-1}{2n}<\frac1{\sqrt{2n}}$
Nilpotent elements in a commutative ring
Limit Rule $\lim f(x)^{g(x)}$
Infinite Cartesian product of countable sets is uncountable
Linear Algebra, eigenvalues and eigenvectors
Show that in a discrete metric space, every subset is both open and closed.
Irreducible polynomial over $\mathbb{Q}$ implies polynomial is irreducible over $\mathbb{Z}$
How Find the $f(x)$ such $\lim_{x\to 1^{-}}\frac{\sum_{n=0}^{\infty}x^{n^2}}{f(x)}=1$
Do eigenvalues of a linear transformation over an infinite dimensional vector space appear in conjugate pairs?
Proof of $\arctan(x) = \arcsin(x/\sqrt{1+x^2})$

Possible Duplicate:

Sum of two closed sets in $\mathbb R$ is closed?

Give an example of two closed sets $A, B \subseteq \mathbb{R}$ such that the set $A + B = \{a + b : a \in A, b \in B\}$ is not closed.

This question appears on an old analysis qual I am studying. I know that both $A, B$ must be unbounded sets, because in an earlier part of the problem I have proved that $A + B$ is closed if either of the two sets are compact. The simplest unbounded and closed subset of $\mathbb{R}$ that I know is $\mathbb{Z}$. So I was starting with $A = \mathbb{Z}$, but I’m not yet able to come up with an appropriate $B$.

- I would like to know an intuitive way to understand a Cauchy sequence and the Cauchy criterion.
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Hints or solutions are greatly appreciated.

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- Prove that $e^x\ge x+1$ for all real $x$

Try $\mathbb Z+\sqrt 2\mathbb Z$.

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