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

[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.