What does it mean to suppress a number in math? I was doing a math problem and it said to "suppress a term of a sequence." Does this mean to decrease or get rid of the term?


Let $x_1,x_2,\ldots,x_n,y_1,\ldots,y_m$ be positive integers, $n,m > 1.$ Assume that $x_1+x_2+\cdots+x_n = y_1+y_2+\cdots+y_m <mn.$ Prove that in the equality $$x_1+x_2+\cdots+x_n = y_1+y_2+\cdots+y_m$$ one can suppress some (but not all) terms in such a way that the equality is still satisfied.

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    $\begingroup$ Could you post the whole problem in which it appeared? It probably just means "remove the term from the sequence", but it's something which could depend on context. $\endgroup$ – Milo Brandt Jan 2 '16 at 23:00
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    $\begingroup$ Indeed, it just means to remove it from the expression. Let $1+1+2+3+4=5+6$, then $1+1+4=6$. This is not specifically a math term, just common sense. $\endgroup$ – Yves Daoust Jan 2 '16 at 23:12
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    $\begingroup$ If you suppress a term how can it still be the same sum? You would have to change some of the terms? $\endgroup$ – Jacob Willis Jan 2 '16 at 23:15
  • $\begingroup$ Oh, I see. You deleted some terms. $\endgroup$ – Jacob Willis Jan 2 '16 at 23:16

In this context, the question might have been worded a little more clearly:

Let $x_1,x_2,\dots,x_n,y_1,\dots,y_m$ be positive integers, where $n,m>1$. Assume that $x_1+\dots+x_n=y_1+\dots+y_m<mn$.

Prove that there exist non-empty proper subsets $A\subset \{1,\dots,n\},B\subset\{1,\dots,m\}$ such that

$$ \sum_{i\in A} x_i=\sum_{j\in B}y_j $$

Justification: Since $x_1+\dots+x_n=y_1+\dots+y_m$, showing that we can remove a non-zero number of terms, but not all, to retain the equality is equivalent to showing that we can choose terms from both sides such that the sums of the terms we choose are the same. Since we choose 'some but not all' of the terms, we know that at least one of the sets of chosen terms must be non empty and at least one must be proper - and then it is not hard to see that in fact they both must be both non-empty and proper.


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