I'm e-discussing this with someone, and I'm not sure if I'm explaining it right.

He uses an analogy that if there is a day A and a day B on an infinite timeline, separated by "five days", it would be possible to move from A to B. I say it's impossible because Infinity+5 = infinity, which is an infinite distance to cross.

but he still holds out. It goes likes this:

him wrote:No, if day A is somewhere on the timeline and B is five days later, you reach B by waiting 5 days. So the universe could well have always been.

Me wrote:NOPE.

Take an infinite timeline, defined as having no beginning or end. Also by definition, the infinite timeline holds an infinite amount of time. Also, by definition, the infinite timeline has no "point" congruous with a beginning or end.

Take A and B. A and B are separated by an amount of time. By definition, there is an infinite amount of time between A and B, since an infinite timeline with no origin holds all time. You can't say "five days separate them" since an infinite timeline includes ALL numbers, so "five days" is meaningless.

Him wrote:if there are infinite days on the timeline, there are infinite different distances between those days, the distance 5 is one of them.

(I also cite references from the link about the Kalam argument, but I guess he doesn't read them.Me wrote:You're not getting what I'm saying, are you?

In an actual infinity the term "five days" is meaningless, because there is no such thing as five days. You need a reference point for five days, and there is none in an infinite timeline. Think of it this way:

In an infinite timeline, A and B are separated by five days. But because they exist on an infinite timelines, the distance IS NOT five days, but rather infinity plus five... which is an infinite distance.

...

...

Lemme make a drawing.

infinity

<--------------------------------------------------------------------------------------------------------->

Divide this in thirds, and we get:

1/3 infinity = infinity 1/3 infinity = infinity 1/3 infinity = infinity

<----------------------------|------------------------------------------|---------------------------------->

Or add to infinity, and we get

infinity + 10 = infinity

<--------------------------------------------------------------------------------------------------------------------------->

Take two arbitrary points, A and B, separated by "five days"

infinity infinity+5 = infinity infinity

<-------------------------(A)------------------------------------(B)------------------------------------>

him wrote: No... I'm not saying I start at 0 with no negative numbers and try to get to infinity. I said we're here, now, and have an infinity behind us and an infinity in front of us. We won't reach any end,( nor a beginning by going back,) because the impossibility of that is what defines infinity. But you can go 5 forward, because that has nothing to do with the infinity behind it and in front of it.

...

...

no, because it's not two random points on the line and 5 days added, it's a period with an infinity behind it, and an infinity in front of it. Like this:

infinity 5 days infinity

<----------------------------------(A to B)------------------------------------>

So, am I explaining this right, or not? I'm obviously not explaining it

*well*.