Partitioning 14

Probability Level 1

We can express 21 as the sum of 5 distinct positive integers : $21=2+3+4+5+7$ .

Can we express 14 as the sum of 5 distinct positive integers?

Yes No

1 solution

Mateo Matijasevick
May 12, 2016

Relevant wiki: Extremal Principle - Definition

The least possible values for $5$ distinct positive integers are $1,2,3,4,5$ . Their sum is $15>14$ , therefore, is not possible to express $14$ as the sum of $5$ distinct positive integers.

why isn't 0 a positive integer?

Happy Hunter - 5 years, 1 month ago

Zero is neither positive nor negative. It's an axiom that $0\notin P$ , $P$ denotes the positive set.

Mateo Matijasevick - 5 years, 1 month ago

I have been taught that 0 is positive AND negative.

Hermengarde Gilneas - 5 years ago

@Hermengarde Gilneas – Unfortunately, you have been taught incorrectly. Zero is nonnegative and also nonpositive integer. Note that the Natural numbers set is different from the Positive numbers set.

Mateo Matijasevick - 5 years ago

Zero is not positive >.<

Davy Ker - 5 years ago

Zero is neutral number

Darmawan Putra Wijaya - 5 years ago

Partitioning 14

1 solution

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