Thinking about infinity

[robvalue]

Thank you

That's an unusual question! You wouldn't be able to write down the "first term", with n=infinity, because that would correspond to the "last term" the other way round. And there isn't one. Neither could you produce the first 10 terms. It would take infinitely many terms before you reached any particular number you wanted to.

But if you're talking about adding the terms in reverse, then the result would be the same. It would just look like:

... + 1/8 + 1/4 + 1/2 = 1

We just have the infinitely many terms at the beginning. We could then rearrange it to be the same as before. When there is only addition, the order you sum things in doesn't matter.

Obviously as you move closer to n=1, each term will double in size instead of halve.

So I'm not entirely sure what you're asking... trying to visualise the summation in reverse? Yes, that's very difficult to imagine or describe, because there is no starting point. Maybe you could create one by using a mapping onto a Riemann Sphere, so that the point n=inf does correspond to a single point on the sphere. (Been a long time since I did something like that.)

PS: Well, technically there is a starting point, the other end of the object... there just isn't a first term to begin the sum with.

[SteveII]

You can't get to infinity by adding finite steps. There is no number + 1 to get you there. You have to distinguish between a real infinite and a potential infinite.

It is also important to note that each "halving" creates a potential and unequal interval that will always add up to a finite number.

[Ignorant]

Thank you

That's an unusual question! You wouldn't be able to write down the "first term", with n=infinity, because that would correspond to the "last term" the other way round. And there isn't one. Neither could you produce the first 10 terms. It would take infinitely many terms before you reached any particular number you wanted to...

Do you think that this makes a geometric series more akin to the coastline problem? I.e. A geometric series as a descriptor of a reality, rather than a reality itself. In short, is a geometric serial division of a line segment a notional infinity (i.e. potential infinity) rather than an infinity of a finite length?

[Ignorant]

You can't get to infinity by adding finite steps. There is no number + 1 to get you there. You have to distinguish between a real infinite and a potential infinite.

It is also important to note that each "halving" creates a potential and unequal interval that will always add up to a finite number.

Sure, "counting to" infinity is incoherent. Counting ad infinitum is coherent, but also never ending (merely notional/potential).

Good point on the halves.

How would you distinguish between a real infinite and a potential infinite?

[LastPoet]

What if I told you there are 'bigger' infinities than N or Q?

I loved that part in my Math Analisys class.

[LastPoet]

Actually #N = #Q, yet both of them are < #R

[Ignorant]

What if I told you there are 'bigger' infinities than N or Q?

I loved that part in my Math Analisys class.

If you told me that, I'd ask you to tell me more! Bigger in what sense?

[LastPoet]

Oh wait, this is Philosophy. Nvm

[LastPoet]

What if I told you there are 'bigger' infinities than N or Q?

I loved that part in my Math Analisys class.

If you told me that, I'd ask you to tell me more! Bigger in what sense?

You can establish a bijective (sp?) Function between N and Q, yet, you cannot establish the same between N and R, you will always leave an infinity of set members out.

[Ignorant]

If you told me that, I'd ask you to tell me more! Bigger in what sense?

You can establish a bijective (sp?) Function between N and Q, yet, you cannot establish the same between N and R, you will always leave an infinity of set members out.

So... infinitely "bigger"? HA! Pretty fascinating. What sort of applications would that have?