Rearrange a series

In this video, I define what it means to rearrange (or reshuffle) a series and show that if a series converges absolutely, then any rearrangement of the series converges to the same limit.
Interesting Consequence: • Riemann Series Theorem
Series Playlist: • Series
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[@jkid1134]

Can't believe this gem is hidden

[@joshuakaufman6787]

Well, not anymore.

[@GuyMichaely]

Why was it hidden?

[@noahtaul]

I predict this is the next video you will make public, maybe sometime in the next week!

[@drpeyam]

You were right!!!

[@kevin326520]

Wonderful video! I was told in class about this fact and to be aware about the conditional convergent series about the re-ordering since in that case, it actually make a difference. However, I have never seen a proof of this. This is actually really interesting and harder than I thought! Thanks!

[@cbbuntz]

My first thought is this is just a passive aggressive way to say blackpenredpen is wrong about the "1/3 of positive integers are even" or whatever

[@dgrandlapinblanc]

Cool. Thank you very much.

[@Kdd160]

nice explain!

[@orenfivel6247]

Is there a video that proofs: if (and maybe only if also) f:ℕ→ℕ is a bijection (i.e., f(n) is the rearrangement or the permutation of the natural #'s), then f(n)→∞ as n→∞?
Is it true also we need to demand that for all finite n∈ ℕ, f(n) must be finite?

[@drpeyam]

You can do it by contradiction, by arguing that in this case f must be bounded

[@orenfivel6247]

@@drpeyam i did it but i wanted to see that kind of video of you

[@andrewren1663]

At 2:50 I think the series of rearrangement \sum (x_n)'= the original series \sum x_n
eq \sum |x_n|?

[@lasithanirmitha321]

Hey Dr Payem, don't we need to take m to be max(N, kp+1,...,kN).

[@drpeyam]

It’s implicit

[@harikishan5690]

cool!!

[@abduhalloqovabdusamad3849]

отличное решение

[@123pok456ey]

The order of this video and the video "Riemann Series Theorem" are rearranged

[@yoav613]

Dr peyam you are taking abig risk here, cause now if you ask your students in the test find the infinite sum.. they can go after the test and tell you my answer is correct i just rearranged it!

[@pierreabbat6157]

The tail of the Ceres? But Ceres isn't a comet!

[@drpeyam]

Hahaha

[@Mathcambo]

Can you teach topology

[@drpeyam]

See topology playlist

[@Mathcambo]

Can you teach matric space

[@Idtelos]

the answer is -1/12...that's my answer to real numbers... I would prove it, but I'll leave that reader. :p

[@drpeyam]

Hahaha