If you aren’t subscribed to the minutephysics YouTube channel, you’re really missing out. With concise explanations (coupled with Crayola marker drawings to illustrate key points), MinutePhysics tackles gravity, dark matter and quantum tunneling (to name a few) in under a minute. Here’s a recent video, “Taming Infinity.”

If you haven’t seen the earlier video referenced in the opening of this one, here is “Adding Past Infinity.”

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Aaahm, the claim in the lower video is just plain wrong, I'm sorry to say. Damaged his credibility immensely.

you can't use the distributive law unquestioningly with infinite series – the series diverges.

See http://en.wikipedia.org/wiki/Mathematical_fallacy…

Henry of Minutephysics here – I'm sorry you're unhappy with this video, but I do in fact research these things: divergent series are actually an old topic in mathematics: check out G.H. Hardy's 1949 book about them ( http://www.archive.org/stream/divergentseries0335… and if you want a more boiled-down approach, try wikipedia.org/wiki/1+2+4+8+…

OK, ahm, I've read that article, and I'm much more confused now than I was before…

The article states: "As a series of real numbers it diverges to infinity, so in the usual sense it has no sum."

"The partial sums of 1 + 2 + 4 + 8 + … are 1, 3, 7, 15, …; since these diverge to infinity, so does the series. Therefore any totally regular summation method gives a sum of infinity"

Yeah, everything in order. Great.

"In a much broader sense, the series is associated with another value besides ∞, namely −1."

Ahh… what? This is mathematics here – associate it with as many values as you like, but ultimately every series has exactly ONE value. Otherwise you get contradictions.

Besides – it's easily provable that the series diverges. The proof that it converges to -1 does very funny things on the other hand, PLUS the same series is listed on the wikipedia page on "mathematical fallacys", with the explanation:

"The error in such "proofs" is the implicit assumption that divergent series obey the ordinary laws of arithmetic."

OK, I'm only a second-year student, and I haven't read Hardy's book – but I know my analysis, and THAT series diverges to infinity. You have to make very strange assumptions or plain errors to come to a different conclusion. And skipping hardy's book, I couldn't find what he sais about that series, but I'm fairly certain he wouldn't proclaim that in standard-analysis that series gives -1… did you check whether he made some remarks as to "non-standard analysis" or "typical errors" or something like that?

This really bugs me now ^^

OK, now about 20 wikipedia-articles later, this all starts to make sense :D

There IS a consistent method of obtaining the results you presented (that I've never heard of before), but it does not use the "classical" limit of a series, but a different summation method that yields different results that are not related to the results of the usual one. To be mathematically precise you'd have to specify exactly which summation method you're using.

But ok, mystery solved, learned something new today ^^

It still seems incredibly weird to me to use the distributive law in a divergent series, though :D

I would second that this is just wrong.

I don't know what Hardy does yet with normal natural Numbers the calculation you are doing is wrong.

If you don't add more to this cliam the way you present it appears to be wrong to me!

(2-1)* 1 = (2 – 1) = 1

(2-1)* 2 = (4 – 2) = 2

(2-1)* 4 = (8 – 4 )= 4

There is a flaw in the math of the video. Check your math please.