B – I understood that that’s how it is, but why does it seem like a wonder of creation to me — meaning, two contradictory things, a thing and its opposite together at once? Isn’t that so? Finite and infinite — aren’t those mutually contradictory?
Help it click for me.

C – But if it has no height at all, wouldn’t it be invisible?

There’s nothing to make click here, because there is no problem. The fact that you are summing a collection of terms does not mean the sum itself has to be infinite. If you can make it click for me why there is a contradiction here, I can try to make it click for you how the contradiction is resolved.
C. In our world it does not exist, and it isn’t invisible. In a two-dimensional world it would exist and could also be visible.

B – I have no idea how to explain that this is not understandable to me. I’m left only to rely on your wisdom, that you claim it makes sense that something finite is made up of an infinite amount?
C – But is the rule brought in the Guide for the Perplexed, that whatever a person can imagine the Creator can do — only about something physically impossible, while what cannot be imagined is logically impossible? Is that not correct? After all, one cannot imagine two dimensions, can one? To see something that has no height at all?

You are inventing baseless assumptions and then having trouble. Note well: not merely unnecessary assumptions, but simply irrational ones. And then you raise difficulties on their basis, in the manner of “one can force a difficulty with enough strain.”
Contradictions cannot be imagined, but not everything that cannot be imagined is a contradiction.

So let’s put it like this:
We need to gather some quantity of items in order to reach some particular, defined, finite quantity.
But if the act of gathering is infinite because the number of items is infinite, then how are we supposed in the end to arrive at something finite?
Please point out where the flaw is here.

Fine, I’ll try one last time. You are looking at it as if I am collecting all the numbers and putting them into a basket, and such a process takes a very long time (infinite time). But there is no process here that unfolds along the time axis. Mathematical addition is a theoretical operation, not a practical one. Therefore there is no problem with adding infinitely many numbers, aside from the question whether they converge to a finite sum. It turns out that in many cases they do. For example, when you add 1/2 plus 1/4 plus 1/8 plus 1/16 and so on to infinity. Note that each term adds to the cumulative sum half of what remains until 1. When you had 1/2, another 1/2 was missing to get to 1. You added 1/4 — that is half the way to 1. Now you have 3/4, and 1/4 is missing until 1. So you add 1/8, which again is half the way to 1. In this way you will never get to more than 1, so it is clear that the infinite sum approaches 1 (approaches meaning equals 1 for our purposes. I remind you that we are not dealing here with the time axis).

Yedai, I don’t want to butt into the thread, only to suggest another explanation of the Rabbi’s words:

In mathematics there is a concept called a “series.” One kind of series is a number series, in which you add a collection of numbers into a sum.

Sometimes the sum is infinite, for example the sum of all the natural numbers: 1+2+3…

Sometimes the sum is actually finite, for example the sum of the first 10 natural numbers: 1+2+3+4+5+6+7+8+9+10

And sometimes, as you asked, the sum *converges* to a finite sum. That is, the value of the sum approaches a finite total. In such a case the series (the expression of the sum) is called a “convergent series” — because the value of the sum approaches a finite number.

In the case you mentioned, 1/2 + 1/4 + 1/8… the series never actually equals 1, but rather approaches 1. The sum of the series approaches 1, because the sum of a series that converges to a finite number by definition *approaches* it.

And as for your question, the addends do not equal 1, and there is no paradox.

There is another topic that may have confused you:
In mathematics, 0.999999… with infinitely many 9s after the decimal point is *defined* to be equal to 1. And that is also not a paradox, but this is not the place to explain it.

Thank you, Jonathan.
On the contrary, if you have something to say also about 0.999999999… then say it — there’s plenty of room here, don’t worry.
In any case, from my point of view it’s the same thing; I don’t know why you said it’s something different.
That is, for some reason I see this — and I’m trying to get out of it and can’t — as something wondrous: that between 1 and 2 there are infinitely many numbers, and that every object can be divided into infinitely many parts.
Something here smells funny to me — some kind of infinity contained within the finite, like the infinite Creator who is found within His finite world.