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.
- 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...)
Experiencing homelessness for one night is very different than the chronic homelessness which people are picturing. That second population is much smaller and way more visible.
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)
Dear god those charts are useless. Different scales all lined up next to each other, no clue as to the value of the bottom of the y axis, no clue as to what the baseline or the peak numbers are, no ability to actually inspect the data... Who are they hiring to do this nonsense at NYT?
They're not intended for comparing chart to chart, there's a table with key numbers below, and links at the bottom to country-by-country, state-by-state, and "look up your city" options.
It's a "look at the spikes" illustration in the spot in an article a big photo would typically go.
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.
