Intereting Posts

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If these two expressions for calculating the prime counting function are equal, why doesn't this work?
On distributions over $\mathbb R$ whose derivatives vanishes
Sufficient condition for a function to be affine
Prove that intervals of the form $(a,b]$, $$, $[a,\infty)$ do not have the fixed point property.
Finding roots of a function with mean value theorem
Why do statisticians like “$n-1$” instead of “$n$”?
If two continuous functions are equal almost everywhere on $$, then they are equal everywhere on $$
Sum of eigenvalues and singular values
Calculate sum of squares of first n odd numbers
Cover of a direct summand
I feel that (physics) notation for tensor calculus is awful. Are there any alternative notations worth looking into?
Prove that a continuous function on a closed interval attains a maximum
How to solve the general sextic equation with Kampé de Fériet functions?
Why is $9$ special in testing divisiblity by $9$ by summing decimal digits? (casting out nines)

**Question:**

Let $a_{i}\in N^{+}$, and the set $A=\{a_{1},a_{2},\cdots,a_{n}\}$,

show that:

- Combinatorics problem (Pigeonhole principle).
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There exists a set $B\subset A$, such that $card(B)>\dfrac{n}{3}$, and that for any $x,y\in B$, then $x+y\notin B$.

This problem is from China Nankai university math competition today. How prove this? Thank you.

Maybe this problem is an old problem, but I can’t find it.

**At last, I find a similar problem: let sets $A=\{1,2,3,\cdots,2n,2n+1\}$, and the sets $B$ such $B\subset A$, and for any $x,y\in B$, then $x+y\notin B$,**

Find the $|B|_{max}$

this problem answer is $|B|_{max}=n+1$. The full solution (Mathematical induction

) can see china BBs:http://zhidao.baidu.com/question/260607678.html

But for this I can’t prove it, Thank you very much

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