Max von Hippel maxvonhippel

## experiments-gpt3.5.txt
Query to 3.5:

> Let 0 < a < 1 and k = ceiling(a/(1-a)).  How can I prove that a <= k/(k+1)?

Response:

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To prove that a ≤ k/(k+1) given that 0 < a < 1 and k = ceiling(a/(1-a)), we can proceed as follows:
	Query to 3.5:

	> Let 0 < a < 1 and k = ceiling(a/(1-a)). How can I prove that a <= k/(k+1)?

	Response:

	---------------


	To prove that a ≤ k/(k+1) given that 0 < a < 1 and k = ceiling(a/(1-a)), we can proceed as follows: