Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive?

Constructive.
To prove that there is a positive integer that equals the sum of the positive integers not exceeding it.
A plain and simple example is

1.1 + 2 = 3

2.10 + 50 + 100 =160

3.6x + 8x +
2x = 16 x



Notice that the sum of the numbers is always greater than the addends. This only proves that any positive sum of any two positive addends will not compare and thus the addends not exceeding a greater value than the sum.

Answered by taskmasters | 2024-06-10

We have proved there is a positive integer that equals the sum of positive integers not exceeding it using specific examples and the formula for the sum of the first n integers. The smallest positive integer that satisfies this condition is 1, demonstrating a constructive proof. The method confirms the existence of the integer through tangible calculations.
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Answered by taskmasters | 2024-09-30