Wait what? (1+2+3+4+...

[Bridge]

It is really Math heavy going. If you don't accept the definition of course then I can't prove anything

Look, I'm not trying to be difficult. I'm not even taking a shot at mathematical limits, I just have a hard time accepting the definition of infinity used in these calculations because it isn't consistent with the real world.

Here's a straightforward question: How long can you continue to divide 1 by half until it reaches 0? And once you "reach" 1/inf, I take it if you continue to divide it by half you just get 0 from that point on, correct? Doesn't that mean that at some point the series - dividing 1 by 2 an infinite amount of times - the value "became" 0? So this supposedly infinite sequence of division can be described like this:

1/2 = 0.5; 0.5/2 = 0.25; 0.25/2 = 0.125 … 0/2 = 0; 0/2 = 0

I'm sorry but that just doesn't make sense to me. It's an infinite sequence of taking something and halving it. How can it disappear?

[BAndrew]

If the points have no size, then how are there any points? And how can you be so sure that there even are infinite of them?

Points are by definition 0 in size. If there were finite (let's say a certain number n) then the lenght of any string would be n*0 = 0

It is really Math heavy going. If you don't accept the definition of course then I can't prove anything

Here's a straightforward question: How long can you continue to divide 1 by half until it reaches 0? And once you "reach" 1/inf, I take it if you continue to divide it by half you just get 0 from that point on, correct? Doesn't that mean that at some point the series - dividing 1 by 2 an infinite amount of times - the value "became" 0? So this supposedly infinite sequence of division can be described like this:

1/2 = 0.5; 0.5/2 = 0.25; 0.25/2 = 0.125 … 0/2 = 0; 0/2 = 0

I'm sorry but that just doesn't make sense to me. It's an infinite sequence of taking something and halving it. How can it disappear?

Not exactly. There is no last step.. It is a fault to think as if there is one. After an infinite amount of division with 2, 1/2 will become 0.

[eliasfrost]

So 0 = infinity?

[BAndrew]

So 0 = infinity?

No. How did you arrrive at this conclusion?
What happens is that 0*infinity is undefined which means it can be anything.

[eliasfrost]

If the points have no size, then how are there any points? And how can you be so sure that there even are infinite of them?

Points are by definition 0 in size. If there were finite (let's say a certain number n) then the lenght of any string would be n*0 = 0

It is really Math heavy going. If you don't accept the definition of course then I can't prove anything

Here's a straightforward question: How long can you continue to divide 1 by half until it reaches 0? And once you "reach" 1/inf, I take it if you continue to divide it by half you just get 0 from that point on, correct? Doesn't that mean that at some point the series - dividing 1 by 2 an infinite amount of times - the value "became" 0? So this supposedly infinite sequence of division can be described like this:

1/2 = 0.5; 0.5/2 = 0.25; 0.25/2 = 0.125 … 0/2 = 0; 0/2 = 0

I'm sorry but that just doesn't make sense to me. It's an infinite sequence of taking something and halving it. How can it disappear?

Not exactly. There is no last step.. It is a fault to think as if there is one. After an infinite amount of division with 2, 1/2 will become 0.

I would say there is no answer since you divide 2 infinite times, but hey what do I know.

[Bridge]

Not exactly. There is no last step.. It is a fault to think as if there is one. After an infinite amount of division with 2, 1/2 will become 0.

I realize that, hence why I put "reach" in quotation marks. But here we are at square one. Why do you say that (1/inf)/2 = 0? It seems to me to be completely unprovable since such a calculation is not possible. Until it is, any evidence provided is purely speculative.

[eliasfrost]

So 0 = infinity?

No. How did you arrrive at this conclusion?
What happens is that 0*infinity is undefined which means it can be anything.

I still don't understand how you can perform a calculation with something unmeasurable. You haven't really told me how that can be done, only that it is done. And it doesn't make any sense to me.

I'm thinking it's more of a philosophical question rather than truth and not something that can be proven but just assumed.

[BAndrew]

I realize that, hence why I put "reach" in quotation marks. But here we are at square one. Why do you say that (1/inf)/2 = 0? It seems to me to be completely unprovable since such a calculation is not possible. Until it is, any evidence provided is purely speculative.

I already said that in order to prove this you have to accept the definition of the limit and work your way through it. If you don't accept the definition then I can't prove anything.

I still don't understand how you can perform a calculation with something unmeasurable. You haven't really told me how that can be done, only that it is done. And it doesn't make any sense to me.

I'm thinking it's more of a philosophical question rather than truth and not something that can be proven but just assumed.

I already told you that multiplying the numbers of points in a line segment (infinite) with the length of one point gives (or could give) you the lenght of a line. segment. This calculation is undefined which means it can't be done straightforward and involves advanced methods.

[Bridge]

I already said that in order to prove this you have to accept the definition of the limit and work your way through it. If you don't accept the definition then I can't prove anything.

Well, it seems we have reached an impasse then. Or rather, we have come infinitely close to it.

[eliasfrost]

But how do you calculate something undefined without simplifying or lose information?