Tootfinder

Rings with common division, common meadows and their conditional equational theories
Jan A Bergstra, John V Tucker
https://arxiv.org/abs/2405.01733 https:/…

Rings with common division, common meadows and their conditional equational theories
We examine the consequences of having a total division operation $\frac{x}{y}$ on commutative rings. We consider two forms of binary division, one derived from a unary inverse, the other defined directly as a general operation; each are made total by setting $1/0$ equal to an error value $\bot$, which is added to the ring. Such totalised divisions we call common divisions. In a field the two forms are equivalent and we have a finite equational axiomatisation $E$ that is complete for the equatio…

In a perfect demonstration of accessibility being better for everyone, when a vegan film uses auto-generated subs in its screener, it might just end up recommending "fortified lamb" for a healthy balanced diet

https://nowthenmagazi…

"A whistle-stop tour of common objections to veganism": I Could Never Go Vegan
When you're covering this much ground, is it possible for a documentary to avoid being disjointed and incomplete?

Wherever we are in the world, we are united by common traditions!: https://benborges.xyz/2024/05/05/wherever-we-are.html

The summatory function of the M\"obius function involving the greatest common divisor
Isao Kiuchi, Sumaia Saad Eddin
https://arxiv.org/abs/2403.02792 …

The summatory function of the Möbius function involving the greatest common divisor
Let $\gcd(m,n)$ denote the greatest common divisor of the positive integers $m$ and $n$, and let $μ$ represent the M\" obius function. For any real number $x>5$, we define the summatory function of the M\" obius function involving the greatest common divisor as $ S_μ(x) := \sum_{mn\leq x} μ(\gcd(m,n)). $ In this paper, we present an asymptotic formula for $S_μ(x)$. Assuming the Riemann Hypothesis, we delve further into the asymptotic behavior of $S_μ(x)$ and derive a mean square estimate f…

Robin Hood: Rising to Honor - Season 1 finale 😲🥹😇
Dramatized historical fiction | Total listening time: 1h 18m
A kingdom burdened by war, taxes, and a tyrannical monarh. As England struggles to carry on in the absence of the good King Richard, other forces begin gathering to grab power. Meanwhile, those who suffer most are the common folk, crus...

Robin Hood: Rising to Honor - Season 1 finale 😲🥹😇
Dramatized historical fiction | Total listening time: 1h 18m A kingdom burdened by war, taxes, and a tyrannical monarh. As England struggles to carry on in the absence of the good King Richard, other forces begin gathering to grab power. Meanwhile, those who suffer most are the common folk, crushed under the weight of excessive taxation and lawlessness. 1 seasons, 7 episodes as of Feb 26, 2024.

"we’ve compiled a list of common marketing terms that seem to mean one thing to consumers and an entirely different thing to some companies."
https://truthinadvertising.org/articles/april-fools-how-some-c…

April Fools: How Some Companies Prank Consumers with Common Marketing Terms - Truth in Advertising
These definitions are a joke.

I’m actually weirdly OK with conspiracy theorists staring at the sun without eye protection.
https://gizmodo.com/conspiracy-theorists-say-stare-at-eclipse-1851387594

Conspiracy Theorists Say Everyone Should Stare at the Eclipse Without Eye Protection
"People can see just by common sense that the sun is not 93 million miles away," one TikToker said.

Common diabetes drug lowers SARS-CoV-2 levels, clinical trial finds:
https://www.cidrap.umn.edu/covid-19/common-diabetes-drug-lowers-sars-cov-2-levels-clinical-trial-finds

I don’t know if you can really see how beautiful the clouds are being illuminated at 1:00 in the morning over Boston Common.

A common refrain from the older folks in my life:
“I asked my father if he considered himself disabled, or someone who had a disability, or was deaf. He answered no, no, and no.”
https://www.lflegal.com/2024/02/accessibility-for-elders/

iPhone Live Captions Wow My 91 Year Old Dad
My 91 year old father Saul Feingold (pictured here) is a role model of aging. He looks forward and not backward. He has no regret for what he can no longer do and is thrilled with what he can. He's lucky and he knows it. When I asked my dad how old he was when he gave up golf he said he never gav