Vipul: Created page with '==Statement== Suppose $A$ and $B$ are subsets of $\mathbb{N}_0$ , both containing $0$ . Define $A + B$ to be the set of all ...'

2009-05-06T21:12:40Z

Created page with '==Statement== Suppose <math>A</math> and <math>B</math> are subsets of <math>\mathbb{N}_0</math>, both containing <math>0</math>. Define <math>A + B</math> to be the set of all ...'

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==Statement==

Suppose <math>A</math> and <math>B</math> are subsets of <math>\mathbb{N}_0</math>, both containing <math>0</math>. Define <math>A + B</math> to be the set of all integers of the form <math>a + b</math>, with <math>a \in A, b\in B</math>. if <math>\sigma</math> denotes the [[fact about::Schnirelmann density]], then:

<math>\sigma(A + B) \ge \min \{ 1, \sigma(A) + \sigma(B) \}</math>.

Equality need not hold.

==Related facts==

===Weaker facts===

* [[Stronger than::Schnirelmann's theorem on Goldbach's conjecture]]

Mann's theorem - Revision history

Vipul: Created page with '==Statement== Suppose A and B are subsets of \mathbb{N}_0, both containing 0. Define A + B to be the set of all ...'

Vipul: Created page with '==Statement== Suppose $A$ and $B$ are subsets of $\mathbb{N}_0$ , both containing $0$ . Define $A + B$ to be the set of all ...'