little grey mouse 🐭

"ordinary induction", which proves a statement φ(𝑛) for all 𝑛∈ℕ, can be generalized: - to any transfinite ordinal. - to any set with a well-ordered relation - to any set with a well-founded relation - to a proper class with a well-founded relation which is set-like.

"Armed with generative AI, a B student can produce A work while turning into a C student." -- Nicholas Carr

I am once again asking people to explain what they mean by "ontologically"

The easiest way to become a bestselling novelist in three easy steps: 1) Write a caricature of a conservative Christian with absolutely no depth. 2) Make sure every reader agrees with your politics. 3) Call it “literary fiction.” Congratulations!

The oldest known Pythagorean triple is recorded on a Babylonian clay tablet from ~1800 BC, written in a sexagesimal number system. Pythagorean triples are among the oldest known solutions of a nonlinear Diophantine equation (integers a,b,c such as a²+b²=c²).

@viroquan1 @AlanRMacLeod i looked at the account - they are virulently anti-spanish.

@AlanRMacLeod @mouse_math Who are these children?

Open. The. Schools.

No Pythagorean triples are isosceles; the ratio of the hypotenuse to a side would be √2, which can't be expressed as the ratio of integers. However infinitely many Pythagorean triples have two legs differing by exactly one: 3² + 4² = 5² 20² + 21² = 29² 119² + 120² = 169²

How it feels

Me: *shares an idea* Them: I hate all of that. Me: *shares an idea* Them: I hate all of that. Me: *shares an idea* Them: I hate all of that. Me: *silence* Them: why dont you ever share your ideas with me? You must hate me. Me: 🔪

Name a parody that was done so well that most people to this day don't realize it was a parody.

@warwick512 the Babylonians had huge tables of pythagorean triples, far more than any practical application would need. pure mathematics!

@mouse_math I'm sure our ancient construction workers, project managers and architects depended on it. Still very handy now.

(3, 4, 5) is the smallest Pythagorean triple and the only one that consists of 3 consecutive integers.

@fie_liz number theory is so strange.

For any primitive Pythagorean triple (a,b,c) with a<b<c: - exactly one of a,b is even and c is odd. - exactly one of a,b is divisible by 3, but never c. - exactly one of a,b,c is divisible by 5. - 60 is the largest number that always divides abc.

i've read some of the diaries of Germans living in Berlin in 1945. what's disturbing is the younger adults still totally believed in National Socialism, even as Germany was being crushed. never underestimate the power of brainwashing at a young age...

@netripy @onlyskypace yes. i immediately recognized the 3-4-5 Pythagorean triple (as did you).

@mouse_math @onlyskypace Easy to solve mentally. The two perfect squares mean the sides of the triangle are 4 and 5 (hypotenuse), so the other side is 3m. (3^2+4^2=5^2) Area of a triangle is half a square, so it's just 3x4/2 = 6 m^2

kalem ve kağıt kullanmadan çözmek imkansız ! x kaçtır ?

@amolitor99 it's a conjecture. Suslin's discoveries pertain to his Operation A which defines the analytic sets, and the theorems: - every Borel set is analytic. - a set of reals is Borel iff both it & its complement are analytic. - there is an analytic set that is not Borel.

@mouse_math that is not a discovery? that's a marvelous problem, but it's not a discovery.

Mikhail Suslin died at age 24 of typhus in the 1919 Moscow epidemic following the Russian Civil War, but not before he made seminal discoveries in the structure of definable sets of real numbers.

2 Oct 1970, 23 year old Farrah Fawcett appeared in the 2nd episode of the Partridge Family, "The Sound of Money", in the role of "Pretty Girl".

The Nazis were not the only ones who operated concentration camps. Britain used them in South Africa and Kenya. In Kenya, the camps were sites for random executions and Interrogation involved stuffing detainees mouth with mud and stomping their throats till they passed out.