1 + 2 + 3 + 4 + 5 + ... = -1/12

https://www.youtube.com/watch?v=w-I6XTVZXww

couldn't finish the video... headache inducing. This is necessarily mathematically incorrect, because:

-A sum isn't done in any particular order, therefore you could very well start with + and - infinite
-all positive integers have an opposite (vice versa), and their sum is always equal to zero. the only integer that is not positive or negative is zero itself.
-it's all based on assumptions.

They seem to obtain that result (which is a tendency, not an actual number, there can be no "=" when infinite is involved) because of the way they count. Which probably makes a lot of sense in physics, but not in maths. Because positive and negative infinite are involved, the result is necessarily an infinite or zero. Not what the result tends to be when they start counting from zero and don't finish (because it's impossible to do so).

overall, they just seem to define a sum as whatever they like whenever they like as long as it gives them the preferred result.
Which is what physicists tend to do with maths to be fair

Just watched the beginning again, because of the title. They specify natural numbers, which is only positive integers.... making this video a flat out lie that seems believable only because it is done by smart people. 0=1 is less incorrect than this nonsense. In this case the correct answer is positive infinity.

In The Field . . it is said that modern physics does not factor infinity into equations. . .

perfect example

He's trying to confuse you by turning binary information into sin waves. Of course if you add waves together you don't get a massive number. What's he's doing is picking the average part of the wave ,so you get some mind blowing number ,but really it's just stupid.

Mareeka wrote: In The Field . . it is said that modern physics does not factor infinity into equations. . .

perfect example

Not really. they make a sum entirely out of natural numbers (positive integers) and obtain a result which is neither positive nor an integer. It's just not possible, infinite or not. In the linked video they create and move parenthesis around... Again, mathematically completely incorrect.

Good fun for them maybe, but highly misleading.


I particularly like these 2 comments:

Bullshit. BULLSHIT!!!

S = 1 - 1 + 1 - 1 + 1 • • • ≠ 0.5

and

I have now had multiple friends ask me to explain to them why this video is wrong. I don't care much that you want to keep things informal and allow for casual fun maths. What bothers me about the video is that you're claiming this is unconditionally true (by the fallacy of authority), and that there's nothing deeper going on for people to read about when in fact there is and the particular proof given in this video is flat out wrong.

It doesn't matter that the "result" is used in physics (physicists are well known to abuse mathematics because the "results" are interesting), or that there is a second video explaining things in more detail (though I don't think it goes far enough to make it clear where the line between truth and falsity was blurred in this video).

What matters is that this video, standing by itself, is spreading massive amounts of misinformation. This is numberphile's blessing and its curse: it's so popular now, and has gained so much influence, that the majority of ignorant viewers (which is the vast majority of all viewers) take what is presented as gospel. You might say that's their problem for being ignorant and not questioning things, but I think it's also seriously dishonest to knowingly do such a thing. To think that mathematicians, who so rarely get as wide an audience as numberphile has, would knowingly lie about mathematics! I can hope it was more of a misunderstanding on the editor's part, but until I see evidence of that, this video has made me lose a lot of respect for numberphile.

Is the set of all natural numbers greater than the set of all even numbers? They're both infinite but there's more 1,2,3,4,5 ... than 2,4,6,8,10 ... . Right? No matter where you stop the first set is always greater.

Since they're both infinite their value would always tend toward positive infinite, making them "equal".
in fact, if you start counting from zero, and take a thousand numbers, the combined values from the "even" set will be greater than those from the natural set.

They show here there are not more numbers between 0 through 2 than there are between 0 through 1; they're the same. But there are more numbers between 0 through 1 than there are of all positive integers. 1,2,3,4,5 ... .

The Divine Totality cannot be taught except from within. Find the Key. OMNI has found it.

Maybe OMNI will throw us a bone and make copies for everybody.

Br. John wrote: Maybe OMNI will throw us a bone and make copies for everybody.

It already has. Love ya brotherXsisterS

Br. John wrote: They show here there are not more numbers between 0 through 2 than there are between 0 through 1; they're the same. But there are more numbers between 0 through 1 than there are of all positive integers. 1,2,3,4,5 ... .

He doesn't prove that. What he discusses is "counting infinity". Natural numbers are countable. real numbers (except for the infinite "few" that are naturals) are not countable.

In fact, all the real numbers between 0 and 1 (which have a decimal representation) can have an "equivalent" natural number... that's how computers actually "write" numbers (in memory). And the notation is generally shorter:

0.00165432 has 23456100

if you take any real, the same can be done:

345.6789 becomes 9876543

For sumbers with no decimal representation it's a bit complicated because there is to my knowledge no way in maths to represent an infinite natural number. But in programming it is possible.

http://www.youtube.com/watch?v=v-pyuaThp-c