erodommoc · HackerTrans

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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.

erodommoc

قبل 3 سنواتdiscuss

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.

erodommoc

قبل 4 سنواتdiscuss

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.

erodommoc

قبل 4 سنواتdiscuss

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)

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