fossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 6 months agoScience memesmander.xyzimagemessage-square20fedilinkarrow-up1262arrow-down114cross-posted to: mathmemes@lemmy.blahaj.zone
arrow-up1248arrow-down1imageScience memesmander.xyzfossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 6 months agomessage-square20fedilinkcross-posted to: mathmemes@lemmy.blahaj.zone
minus-squareeestileib@sh.itjust.workslinkfedilinkEnglisharrow-up5·6 months agoShould be anything less than a harmonic decrease (that is, the nth centaur is 1/n the size of the original). The harmonic series is the slowest-diverging series.
minus-squareKogasa@programming.devlinkfedilinkEnglisharrow-up1·6 months agoThe assumption is that the size decreases geometrically, which is reasonable for this kind of self similarity. You can’t just say “less than harmonic” though, I mean 1/(2n) is “slower”.
minus-squareeestileib@sh.itjust.workslinkfedilinkEnglisharrow-up2·6 months agoEh, that’s just 1/2 of the harmonic sum, which diverges.
minus-squareKogasa@programming.devlinkfedilinkEnglisharrow-up2·6 months agoYes, but it proves that termwise comparison with the harmonic series isn’t sufficient to tell if a series diverges.
minus-squareeestileib@sh.itjust.workslinkfedilinkEnglisharrow-up3·6 months agoVery well, today I accede to your superior pedantry. But one day I shall return!
Should be anything less than a harmonic decrease (that is, the nth centaur is 1/n the size of the original).
The harmonic series is the slowest-diverging series.
The assumption is that the size decreases geometrically, which is reasonable for this kind of self similarity. You can’t just say “less than harmonic” though, I mean 1/(2n) is “slower”.
Eh, that’s just 1/2 of the harmonic sum, which diverges.
Yes, but it proves that termwise comparison with the harmonic series isn’t sufficient to tell if a series diverges.
Very well, today I accede to your superior pedantry.
But one day I shall return!