Talk:Restriction of Associative Operation is Associative

"Revert"

I have essentially reverted this page to the 2015-03-31 revision, that is, changing the conclusion from $T$ being a semigroup back to simply the restriction of $\circ$ is associative, and retracting the requirement of $\struct {S, \circ}$ being a semigroup. The reasons are as follows:

1. The name of this page.

2. While the conclusion that $T$ is a semigroup is true, that proof is shown in Subsemigroup Closure Test.

3. Of the 20-ish pages that use this result, all use only the associativity result, but not that $T$ is a semigroup. Most of those pages are dedicated to showing each axiom of their respective structures are satisfied, instead of using a "structure with this property is another structure" style proof.

--RandomUndergrad (talk) 12:46, 9 March 2022 (UTC)

Thanks, good job. It should never have been amended in the first place. I should have changed it back as soon as we evicted the perpetrator, but for some reason we didn't. --prime mover (talk) 17:28, 9 March 2022 (UTC)