every positive rational number can be written as a finite sum of distinct numbers of the form 1/n where n is natural

Question

every positive rational number can be written as a finite sum of distinct numbers of the form 1/n where n is natural

I don't quite understand this question. Actually, what does distinct numbers of the form $1/n$ mean? Does it mean $m(1/n)$ or $(1/n)^m$? Can anyone express $17/15$ as an example?

it means: $\forall q \in \mathbb{Q}$ there exists $A \subseteq \mathbb{N}$ such that $q = \sum_{n \in A} \frac{1}{n}$. — mathworker21, Nov 12 '18 at 10:38
For example: $2/3 = 1/2 + 1/6$. And $17/15 = 1/1 + 1/10 + 1/30$. — Mees de Vries, Nov 12 '18 at 10:41
I came up with that example by (basically) trial and error. There are algorithms and proofs of existence on the linked Wikipedia page. — Mees de Vries, Nov 12 '18 at 11:18

score 2 · Accepted Answer · answered Nov 12 '18 at 10:40

2

No, "distinct numbers of the form $\frac{1}{n}$" refers to numbers like $\frac{1}{2}$, $\frac{1}{3}$, $\frac{1}{4}$, etc. There is no "m" as numerator or exponent. The "distinct" means that all the denominators are different.

answered Nov 12 '18 at 10:40

user247327

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every positive rational number can be written as a finite sum of distinct numbers of the form 1/n where n is natural

1 Answers1