erodommoc

Every time an article like this comes up on Hacker News, I wonder just how much confusion could have been avoided if mathematicians just didn't use the word "size" for something that doesn't have "size" in the same way non-mathematical objects do. Just call it "larger cardinality" or something.

Off by over 5x:

- The U.S. Department of Housing and Urban Development (HUD) today released its 2022 Annual Homeless Assessment Report (AHAR) Part 1 to Congress. The report found 582,462 people were experiencing homelessness on a single night in January 2022 (https://www.hud.gov/press/press_releases_media_advisories/HU...)

- Largest college football stadium: Michigan Stadium (Ann Arbor, Mich.) 107,601 (https://www.ncaa.com/news/football/article/2018-07-30/25-big...)

- The population of Baltimore, MD is 576,498 as of the last census, so would be a closer point of comparison.

I feel like I'm missing something here - wouldn't the shortest program that returns the integer i just be "return i"? The length of that seems pretty easy to compute.

Right - every time you add a '9', the difference gets smaller, but it's still there, it never completely goes away no matter how arbitrarily large number of times you repeat the process. However, most math doesn't treat '0.99 repeating' as an algorithm to approximate a number, but as an _actual number_. There is no 'adding another 9', all of the infinite number of 9's are added at the same time. It's (at least to me) very different from the intuitive meaning of '0.99...', but if you treat it as the mathematical object '0.99...', not as 'start with 0.99, and keep adding 9's as necessary to approximate', then 0.999999... does in fact equal 1.00000... because it's impossible to compute a number in between them. (edited to hopefully improve the explanation)

Here's the charts for a number of states in the US. It's pretty dramatic. https://www.nytimes.com/interactive/2020/04/28/us/coronaviru...

And this I think is the real issue. When someone says that 0.999... = 1.0, what they are saying is that this is true given a number of assumptions that we are taking for granted that would not be obvious to a non-mathematician. There's a lot of math hiding in those '...'.

Right, but many things make sense for finite sets that don't make sense for infinite sets. Just because you can extend that definition doesn't mean that it's "true" for infinite sets.

Well, the answer is equal because of how you define equality of infinite sets (one-to-one and onto). It's a very useful definition, but it's hardly the only possible definition.

Treesize (https://www.jam-software.com/treesize_free/) is a great one for Windows.

I see what you did there...

Of course, this is all based on a single study from the 1960's (Solomon, David, "Accidents on main rural highways related to speed, driver, and vehicle"), which has been pretty thoroughly debunked (http://casr.adelaide.edu.au/ruralspeed/RURALSPEED.PDF).

So if you want to change the world, blindly accept orders from authority figures, no matter how inane? Sure...

This seems to come up over and over again, and it always comes down to what assumptions you start with. If you accept all of the axioms and methods, the proof holds. If you don't, it doesn't. Articles like this one, aimed at an audience that already assumes that its techniques are valid, are never going to convince a non-mathematical audience that doesn't know what the basic assumptions are, because that's not their goal.