I'm not sure if you can use the words, "more" or "less" or "larger" or "smaller" and so on, in dealing with numbers. It doesn't seem reasonable to me to do so because of infinity. Of course you can use those words in a practical application, but when dealing with theories of infinity, it seems perhaps those things don't exist, or perhaps we just don't have the correct terminology to describe what we're trying to say. ========= OH, it figures I stopped the video to make this comment right before your mentioning Galileo's conclusion. Ugh. Well I'm glad at least I had the same conclusion.

no sane or mentally well person were made for this…
thankfully i am neither

Let's not also forget that in mathematics 0 doesn't exist..as a number

I am not buying this whole concept of bigger infinities. It is illogical.

I lost u after 20 min😅

Why can’t we well order the reals by first. Decimal length, magnitude, then sign

All positives are followed by their negative so I’ll just the positive values
0,1,2,3,4,5,6,7,8,9,0.1,0.2,0.3

So first from 0 to 1 is 0.1 first positive is 1

For irrationals they’re ordered by magnitude square root of 2 before pi

From pi to sqrt(11): 3.2,3.3,3.14,3.15…

This seems well ordered to me

The issue with duplication of the balls is because axiom of choice relays on your choice never being the same, also you are putting the ball and make it move in 4 directions.
Okey if you have an origin point and each mapped point can be an origin, then that means when you picking up a direction where the ball to move if you have infinite points you have infinite directions too, not just four, if we see a set of numbers with a point of origin or starting point then exactly the opposite result of our origin is the end. While infinity doesn't theoretically have beginning or an end, because it is infinite. If we are to pick a starting point of a set then exactly the opposite of that set should be the end, we don't know where that is, with that in mind if you have +numbers and -numbers, then 0 is the only number where you have no positive or negative origin point because 0 is 0, therefore if you align all numbers in a set at some point in time they should come back to 0, but if thats true then you have measurable quantity by a definition of a modern math solutions. The paradox we are facing here is… you cannot measure infinity but to prove infinity exists that means it is measurable.

You know what always confused me…
Realistically, it seems like our conception of time MUST be inherently flawed due to the fact that time elapses at all

Consider this, I propose that there MUST be a limit to infinity or infinity doesn't exist..
if there TRULY are an infinite amount of real numbers, would've that entail that an infinite amount of "time" would HAVE to elapse before progressing to the next "second"

If we could break a single second down, & take account every single "infinite" real number existing within each second, then what EXACTLY triggers the inevitable switch from 1.99999999..∞.. to 2.0?

I suppose what I'm asking is, with our current understanding of numerology & mathematics, how do we account for the passage of time when our way of tracking time infers that an infinite series of "0.999's" could theoretically continue on forever before changing to 1.0?

Having difficulties understanding how all positive integers first, then all negative is well ordered. Suppose I have a mapping 0,1,-1,2,-2,… I could name any arbitrary integer, positive or negative (-345697845594587498 maybe). Just by counting for long enough I would arrive at this number. In the other case, all positive first, I just have to name -1. I will never arrive at it. Where is the supposed definitive starting point?

So 0 isn't considerd a real Number by it's own? Edit. Also i thought we already know that Infinitys can exist in other Infinitys … Im talking about Infinity in General Not Just in "math" wich is weard since everything could be explained in / with numbers …

Only "almost"?? I'm pretty sure that guy Donald broke ALL the math… 🤔🤦🤠😭🥳😵

In the end, everything is an illusion…

I need a Veratasium video just to understand the already broken down explanation

Holy cow! 8m views. This is insane. Feel like there are much more interesting people in the world then I ever realized. Where are all these interesting people hiding?!