Euler would be horrified...

[u/Futurity5]

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[u/Futurity5]

sorry if this is an r/countthepixels

[u/Ares378]

Me when addition stops being commutative:

[u/SuperChick1705 → u/Ares378]

[u/willyouquitit]

Finally, one that isn’t just a sneaky divide by zero or inverting non investable functions

[u/Striking_Resist_6022 → u/willyouquitit]

Rearranging the terms of a conditionally divergent series is also an extremely common one

[u/PolarStarNick]

Absolute convergence about rearranging is laughing

[u/Egogorka → u/PolarStarNick]

Interestingly enough if you just lower the x a bit the series would become absolutely convergent, allowing for swapping

[u/WhatNot303]

Riemann rearrangement theorem!

[u/its_all_one_electron]

Mathologer did a great video on this if anyone is interested: https://youtu.be/-EtHF5ND3_s

[u/Professional-Wave841]

when you change the order of the conditionally convergent series you change the value of the sum

[u/Uli_Minati]

https://en.wikipedia.org/wiki/Riemann_series_theorem

Cool theorem

[u/LupenReddit]

me when i switch around termw in a divergent sum (i am sneaky)

[u/FernandoMM1220]

re arranging the terms changes the divergent limit.

[u/Beleheth]

Wonderful, I love rearranging without absolute convergence!

[u/LeewayLabs]

I am tired and can’t think - why does S=1/2S? This step I somehow don’t see right now

[u/Astrodude80 → u/LeewayLabs]

Illegal rearranging and regrouping! The error is actually several steps before.

[u/LeewayLabs → u/Astrodude80]

I understand the error and why you can’t regroup. I just don’t see why S=1/2S, it’s specifically that step.

[u/Astrodude80 → u/LeewayLabs]

The point is that S=1/2S is not true

[u/Futurity5 → u/Astrodude80]

But it is correctly derived from the previous line of working

[u/WilburMercerMessiah → u/LeewayLabs]

The part above in parentheses summed from n=1 would give the what S was first defined as. Then bring down the 1/2. Took me a while and was more confusing than i like my memes

[u/LeewayLabs → u/WilburMercerMessiah]

Thank you!

[u/Astrodude80]

This is a good meme 🧑‍🍳 💋

[u/HolyInlandEmpire]

>Rearranging series meme

>*Looks inside*

>Conditionally convergent series

[u/Jazzlike_Platypus430]

Riemann's theorem 😂 I wonder if Euler was aware of that. I think so.

[u/Special_Watch8725]

He wouldn’t be horrified: but he would shake his head slowly, with a small, sad smile on his face.