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The Peano Axioms: Building Blocks of Arithmetic

https://principlesofcryptography.com/number-theory-primer-an-axiomatic-study-of-natural-numbers-peano-axioms/

Oh, look! New Scientist has discovered basic #arithmetic is hard! Who knew counting people was such a complex endeavor? Next up: "Have We Underestimated the Total Number of Toasters?"
https://www.newscientist.com/article/2472604-have-we-vastly-underestimated-the-total-number-of-people-on-earth/ #NewScientist #Complexity #CountingPeople #Toasters #Research #Humor #HackerNews #ngated

Ah, the classic tale of the programmer who saw the light and returned to the glorious '90s to worship at the altar of #C. After 20 years of #Rails, our hero ditches modern convenience for C's sweet embrace, because who needs progress when you can dive into the abyss of #pointer #arithmetic and null pointer dereferences?
https://www.kmx.io/blog/why-stopped-everything-and-started-writing-C-again #programming #nostalgia #programming #developer #tech #humor #HackerNews #ngated

After looking for a long time, I finally found this #Sliderule, which belonged to my late father. Some of you will know that these #devices were used, before the advent of digital #Calculators, to perform #arithmetic operations such as #multiplication and #division to about three significant figures, by #scientists and #engineers.

#Mathematics #Computation (1/2)

Taming Floating-Point Sums

https://orlp.net/blog/taming-float-sums/

“The most savage controversies are those about matters as to which there is no good evidence either way. Persecution is used in theology, not in arithmetic, because in arithmetic there is knowledge, but in theology there is only opinion.”

— Bertrand Russell (Unpopular Essays)...
#quote #philosophy #BertrandRussell #knowledge #opinion #arithmetic #theology

#StephenWolfram - Is #Mathematics #Invented or #Discovered?

https://www.youtube.com/watch?v=RlMMeqO7wOI

#decompwlj It's a decomposition of positive integers. The weight is the smallest such that in the Euclidean division of a number by its weight, the remainder is the jump (first difference, gap). The quotient will be the level. So to decompose a(n), we need a(n+1) with a(n+1)>a(n) (strictly increasing sequence), the decomposition is possible if a(n+1)<3/2×a(n) and we have the unique decomposition a(n) = weight × level + jump.

We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. For natural numbers, the weight is the smallest prime factor of (n-1) and the level is the largest proper divisor of (n-1). Natural numbers classified by level are the (primes + 1) and natural numbers classified by weight are the (composites +1).

For prime numbers, this decomposition led to a new classification of primes. Primes classified by weight follow Legendre conjecture and i conjecture that primes classified by level rarefy. I think this conjecture is very important for the distribution of primes.

It's easy to see and prove that lesser of twin primes (>3) have a weight of 3. So the twin primes conjecture can be rewritten: there are infinitely many primes that have a weight of 3.

I am not mathematician so i decompose sequences to promote my vision of numbers. By doing these decompositions, i apply a kind of sieve on each sequences.

https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump