Math peeps explain this to me

[Chaotic42]

I said I wouldn't get into this, but what the hell. For those of you willing to buy that 1-1+1-1... is equal to 0.5, without looking it up, what would you think 1+0-1+1+0-1... is equal to?

No cheating.

The answer is 2/3 by the way

 

[purbeast0]

The answer is 2/3 by the way

its equal to 0 or -1, depending when you stop the ...

 

[Chaotic42]

its equal to 0 or -1, depending when you stop the ...

Which is my point. The OP depends on 1-1+1-1... being equal to 0.5, which depends on using an alternate definition called a Cesaro summation. The Cesaro sum 1+0-1... is 2/3.

So the sum of 1-1+1-1... is not 0.5. It is undefined for the traditional definition of summation. That's what bothers me about the video.

 

[zinfamous]

"We don't know so we take the average"

I'm sure they are right, far smarter than I am, but that just feels like "Eh, math, close enough". LOL

I'm with you.

But I also kinda get it. They are talking infinity, so there really isn't an end, or a specific point in the string where it is defined. I think quantum physics, and I think atoms that are here and there at the same time.

If the state of the problem is either 1 or zero, depending on when you say "Stop," it never really is 1 or zero, because you saying "stop" is actually arbitrary--not the fact that you decide to define the sum as 1/2. It is 1/2, because it can only be 1/2, as it is most closely approximated as the ave value of it's 2 constant states.

er, something like that. I dunno. I hate math.

 

[Bird222]

Which is my point. The OP depends on 1-1+1-1... being equal to 0.5, which depends on using an alternate definition called a Cesaro summation. The Cesaro sum 1+0-1... is 2/3.

So the sum of 1-1+1-1... is not 0.5. It is undefined for the traditional definition of summation. That's what bothers me about the video.

Can you explain how 1+0-1... is 2/3 and how 1-1+1.. is undefined?

 

[Puppies04]

Can you explain how 1+0-1... is 2/3 and how 1-1+1.. is undefined?

He isn't saying that though is he.

 

[DrPizza]

Can you explain how 1+0-1... is 2/3 and how 1-1+1.. is undefined?

He's saying that 1-1+1-1+... is not really 0.5. But, for the people who think that it's 0.5, then by their exact same mathematics, 1+0-1+1+0-1+... = 2/3.

If you look at partial sums,
sum of 1 term (S_1) = 1
S_2 = 1
S_3 = 0.
S_4 = 1
S_5 = 1
S_6 = 0.

2/3 of the time, it's 1, 1/3 of the time, it's 0. So, a weighted average... the sum is 2/3. (nonsense.)