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#arithmetic

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Khurram Wadee ✅<p>After looking for a long time, I finally found this <a href="https://mastodon.org.uk/tags/Sliderule" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Sliderule</span></a>, which belonged to my late father. Some of you will know that these <a href="https://mastodon.org.uk/tags/devices" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>devices</span></a> were used, before the advent of digital <a href="https://mastodon.org.uk/tags/Calculators" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Calculators</span></a>, to perform <a href="https://mastodon.org.uk/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> operations such as <a href="https://mastodon.org.uk/tags/multiplication" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>multiplication</span></a> and <a href="https://mastodon.org.uk/tags/division" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>division</span></a> to about three significant figures, by <a href="https://mastodon.org.uk/tags/scientists" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>scientists</span></a> and <a href="https://mastodon.org.uk/tags/engineers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>engineers</span></a>.</p><p><a href="https://mastodon.org.uk/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Mathematics</span></a> <a href="https://mastodon.org.uk/tags/Computation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Computation</span></a> (1/2)</p>
formuchdeliberation<p>“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.”</p><p>— Bertrand Russell (Unpopular Essays)...<br><a href="https://mastodon.world/tags/quote" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>quote</span></a> <a href="https://mastodon.world/tags/philosophy" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>philosophy</span></a> <a href="https://mastodon.world/tags/BertrandRussell" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>BertrandRussell</span></a> <a href="https://mastodon.world/tags/knowledge" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>knowledge</span></a> <a href="https://mastodon.world/tags/opinion" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>opinion</span></a> <a href="https://mastodon.world/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> <a href="https://mastodon.world/tags/theology" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theology</span></a></p>
Rémi Eismann<p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> ➡️ 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)&gt;a(n) (strictly increasing sequence), the decomposition is possible if a(n+1)&lt;3/2×a(n) and we have the unique decomposition a(n) = weight × level + jump.</p><p>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).</p><p>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.</p><p>It's easy to see and prove that lesser of twin primes (&gt;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.</p><p>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.</p><p>➡️ <a href="https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Decomposition_in</span><span class="invisible">to_weight_*_level_%2B_jump</span></a></p><p><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/sequences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequences</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NumberTheory</span></a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PrimeNumbers</span></a> <a href="https://mathstodon.xyz/tags/JavaScript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JavaScript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/classification" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>classification</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>primes</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a> <a href="https://mathstodon.xyz/tags/integer" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>integer</span></a> <a href="https://mathstodon.xyz/tags/decomposition" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decomposition</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/theory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theory</span></a> <a href="https://mathstodon.xyz/tags/equation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>equation</span></a> <a href="https://mathstodon.xyz/tags/graphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphs</span></a> <a href="https://mathstodon.xyz/tags/sieve" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sieve</span></a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fundamental</span></a> <a href="https://mathstodon.xyz/tags/theorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theorem</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a></p>
💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱<p><span class="h-card"><a href="https://veganism.social/@beforewisdom" class="u-url mention" rel="nofollow noopener" target="_blank">@<span>beforewisdom</span></a></span> <br>Australian actually, but I have taught both the U.K. and N.S.W. curricucula. Some of the terminology is different, but of course all the rules are exactly the same (as they are everywhere).</p><p>Interesting that you mention <a href="https://dotnet.social/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> as what I've found is the students who say they hate <a href="https://dotnet.social/tags/Maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Maths</span></a> are the students who actually are lacking in their arithmetic skills! (so OF COURSE they are struggling with the harder stuff). Once they're up to speed with that they don't hate <a href="https://dotnet.social/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> anymore!</p>