Yeah, if you use an arbitrary standardized measuring stick, the problem goes away, as it is no longer infinite.

Still a fun thought experiment to demonstrate how unintuitive infinities are!

Anyway, major kudos to you for engaging with this thread in good faith! That is so rare these days, I barely venture to comment anymore. Respect.

… and thank you for the opportunity to share a weird math fact!

And it may very well be true, but we can’t prove it mathematically.

Exactly! It is unintuitive, but there are as many infinite elements of the set of all real numbers between 0 and 1, as there are in the set between 0 and 100.

I hope this demonstrates what the people here arguing for the paradox are saying, to the people who are arguing that one is obviously longer.

Just because something is obvious, doesn’t make it true :)

Its true that not all infinities are equal, but the way we determine which infinities are larger is as follows

Say you have two infinite sets: A and B A is the set of integers B is the set of positive integers

Now, based on your argument, Asia has the largest infinite coastline in the same way A contains more numbers than B, right?

Well that’s not how infinity works. |B| = |A| surprisingly.

The test you can use to see if one infinity is bigger than another is thus:

Can you take each element of A, and assign a unique member of B to it? If so, they’re the same order of infinity.

As an example where you can’t do this, and therefore the infinite sets are truely of different sizes, is the real numbers vs the integers. Go ahead, try to label every real number with an integer, I’ll wait.

I drink alcohol instead.

I am not a good role model.

Ummm…

I use Arch btw 🙃

Punch the keys for god’s sake!

And what I’m saying is it doesn’t take more time to opt out in my experience. Its just as quick to get manually verified as to be biometrically scanned.

¯\(ツ)/¯ maybe, but as long as I have the option and it’s not tedious to do so (which is the case), I’m gonna opt out and encourage others to do so. Fair enough if your perspective is you want to accept whatever new security theater data collection is implemented in exchange for some perceived convenience. Making your case here with me in this conversation has taken more effort on your part than opting out of facial recognition at the security checkpoint in an airport would have, and I find that fact amusingly ironic.

I’ve been in and out of DFW, BOS, and JFK since these facial recognition scanners went in and I can tell you with a great deal of confidence that there’s no additional wait time, or queue, or anything else if you opt out. There’s a TSA agent right next to the scanner who collects your ID whether you get scanned or not. That’s the same person who otherwise just checks it if you opt out. What are you even on about? Maybe its different at some airports, but I’ve been opting out every time I fly and it’s no big deal.

Actually no, they look at your face and your ID, make sure the information matches, and move you along. No secondary inspection, no difference except you didn’t get scanned with facial recognition. It’s the same process as before facial recognition was implemented.

Why even write that comment?