I guess that I have succeeded with delivering mind-blowing fact. And that one bit was 'assumed' as in "we don't want to make this video a boring 30 minute slog so just trust us that we know what we are doing" not "we have just arbitrarily decided on that one result and will continue onward without regard if that's true or not".

But it is true. It's not all that counter-intuitive as it might seem, but it forces you to stop assuming that what you know about finite operations hold true. Article.

Consider this:

Sum of all numbers from k = 0 up to k -> Infinity (k is assumed a natural number) in form of: 1/k! (inverse of a factorial of k).

You are adding 1 + 1 + 1/2 + 1/6 + 1/24 + 1/120 + … and you are getting Euler's number.

Think about it. You are adding rational numbers but get an irrational number as the result! It defies normal finite-element reasoning. I mean, it's not like I can add two rational numbers and get something like square root of 3, right?

Mathematics is full of such situations where you can't allow yourself to just go on intuition, but need to have a strong formal backing. I can do a formal reasoning for you if you are actually interested.