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…
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…
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…
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…
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…
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,…
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…
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…
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…
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…
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…
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,…