The sum of all positive integers (1,2,3,4,5,6...) = -1/12

[The Impractical Engineer]

This is a controversial topic in the math community.

At first it seems silly, but there are numerous websites and videos 'proving this'. There are also numerous websites and videos against the claim.

I think the sum off all positive integers converges towards infinity.

What do you think?

[Big Pharma]

I agree that it probably converges toward infinity, but I'm sure that there's a higher plane of math that says otherwise.

[L1qu1dator]

I tihnk you're asking a wrong question for the offtopic :P

This is why I lost interest in math, it gets ridiculous when going deeper into it.

[King Narwhal]

How could it end up as a negative number if it's just adding positive numbers? Doesn't make much sense to me tbh.

[Gus the Crocodile]

I don't really appreciate the Numberphile video that sparked this off. It relies on specific, unusual definitions of "equals" and perhaps "sum", and pretty much completely fails to acknowledge that. I agree with the view I've read in a few articles, that presenting maths as if it's a weird inconsistent, "mind-bending" space is pretty counterproductive if maths education is your goal.

[The Impractical Engineer]

Publicado originalmente por Captain Narwhal:

How could it end up as a negative number if it's just adding positive numbers? Doesn't make much sense to me tbh.

Here is the video that sparked this whole controversy (although there was an Indian Mathematician that made this claim in 1913):

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

Here is a second video that argues against it:

https://www.youtube.com/watch?v=YuIIjLr6vUA

You will need a high school level-of-math understanding to at least follow along. Since it gets pretty heavy near the end.

[The Impractical Engineer]

Publicado originalmente por Gus the Crocodile:

I don't really appreciate the Numberphile video that sparked this off. It relies on specific, unusual definitions of "equals" and perhaps "sum", and pretty much completely fails to acknowledge that. I agree with the view I've read in a few articles, that presenting maths as if it's a weird inconsistent, "mind-bending" space is pretty counterproductive if maths education is your goal.

Yeah. They claim that 1-1+1-1+1-1+1... is equal to 1/2. Which it is not. It either equals one or 0, depending on where you stop.

[Blargo]

Wouldn't we first need to have a limit to how large numbers can get before we can calculate the sum of all positive integers?

[The Impractical Engineer]

Publicado originalmente por Dxpress:

Wouldn't we first need to have a limit to how large numbers can get before we can calculate the sum of all positive integers?

No, since for every 'highest' number n, there is a greater number than n; n + 1.

[Blargo]

Publicado originalmente por The Impractical Engineer:

Publicado originalmente por Dxpress:

Wouldn't we first need to have a limit to how large numbers can get before we can calculate the sum of all positive integers?

No, since for every 'highest' number n, there is a greater number than n; n + 1.

That's what I mean. There is no absolute limit to how high numbers can get, so it can't be possible to add all positive integers when there isn't an actual set amount of positive integers to add.

[The Impractical Engineer]

Publicado originalmente por Dxpress:

Publicado originalmente por The Impractical Engineer:

No, since for every 'highest' number n, there is a greater number than n; n + 1.

That's what I mean. There is no absolute limit to how high numbers can get, so it can't be possible to add all positive integers when there isn't an actual set amount of positive integers to add.

1/2 + 1/4 + 1/8 + 1/16 + 1/32.............

this series converges towards 1, obviously.

as with 1+2+3+4+5.................

That series converges towards infinity.

[Knee]

Publicado originalmente por Freqsync:

Abbot and Costello 7x13=28

Look it up.

All those time travellers trying to change history leave this alone.

A MAN OF CULTURE

[chiefputsilao✖️ping]

1/2 + 1/14 + 1/8 + 1/16 + 1/32.............

this series converges towards 1, obviously.

the sum of positive fractions is less than 1

[chiefputsilao✖️ping]

the sum of all positive integers is infinity + 1

[The Impractical Engineer]

Publicado originalmente por chiefputsi✖✖✖ 上 没什么 老挝:

1/2 + 1/14 + 1/8 + 1/16 + 1/32.............

this series converges towards 1, obviously.

the sum of positive fractions is less than 1

These fractions are not 'all' fractions. These fractions have denominators 2^x. Also, I Meant plus a quarter, not a fourteenth, but anyway:

1/2 + 1/4 = 0.75

1/2 + 1/4 + 1/8 = 0.875

...

If we continue this series the value will get closer and closer to 1.

[The Impractical Engineer]

Publicado originalmente por chiefputsi✖✖✖ 上 没什么 老挝:

the sum of all positive integers is infinity + 1

I'm beginning to think you are either trolling or are still in primary school.

Infinity is not a number, and thus cannot be used in an equation.