I'm not trying to be flippant, although it may come off that way: why does any of this matter?
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How many real numbers exist? New proof moves closer to an answer
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Re: How many real numbers exist? New proof moves closer to an answer
#12I'm not trying to be flippant, although it may come off that way: why does any of this matter?
It took many years to understand that!
It’s not a flippant question at all.
The answer is, it doesn’t matter. And that’s the joy of it.
It wasn’t until I got into ML that I learned the value of doing unimportant work. When you’re free to think about inconsequential matters very seriously, you end up discovering so many useful things. It was how I independently rediscovered what is apparently called the Discrete Hartley Transform.
You have a vague notion that what you’re doing might be important, but it’s not the focus. It matters because it’s fun in a way that nothing else can be.
Of course, the more serious folk won’t admit it’s fun. It’s serious work. And they’re not wrong; nobody’s fooling around. Our time is every bit as precious as an executive’s.
But their goal is to change the world. Ours — or mine, at least — is to know the truth of a thing that most people don’t know.
Re: How many real numbers exist? New proof moves closer to an answer
#13I'm not trying to be flippant, although it may come off that way: why does any of this matter?
It took many years to understand that! It’s not a flippant question at all. The answer is, it doesn’t matter. And that’s the joy of it. It wasn’t until I got into ML that I learned the value of doing unimportant work. When you’re free to think about inconsequential matters very seriously, you end up discovering so many useful things. It was how I independently rediscovered what is apparently called the Discrete Hartl…
> it doesn’t matter
It doesn't matter yet. Applications of pure math happen downstream decades or centuries later. It's hard to predict the impact.
Re: How many real numbers exist? New proof moves closer to an answer
#14I'm not trying to be flippant, although it may come off that way: why does any of this matter?
I think you'd have to say exactly what you mean by "matter".
At one point in my life I felt like the continuum hypothesis was the most important question in the world. Now I'm mostly concerned about finite material issues, e.g. my health. I think a good argument can be made why either of them matter much more than the other.
Re: How many real numbers exist? New proof moves closer to an answer
#15I'm not trying to be flippant, although it may come off that way: why does any of this matter?
It took many years to understand that! It’s not a flippant question at all. The answer is, it doesn’t matter. And that’s the joy of it. It wasn’t until I got into ML that I learned the value of doing unimportant work. When you’re free to think about inconsequential matters very seriously, you end up discovering so many useful things. It was how I independently rediscovered what is apparently called the Discrete Hartl…
Lololol. U gay.
Re: How many real numbers exist? New proof moves closer to an answer
#16I'm not trying to be flippant, although it may come off that way: why does any of this matter?
This is kind of the equivalent of asking why does your life matter?
Re: How many real numbers exist? New proof moves closer to an answer
#17> "Not all infinities are equal"
In other words, there are different categories of infinite, and it might be inappropriate to represent infinity with just one symbol! This article is about how many types of infinity might exist.
I was taught there is countably and uncountably infinite. Integers are countably infinite because the number of integers between any two numbers if finite. Real numbers are uncountably infinite because there are infinite numbers between any two real numbers.
Re: How many real numbers exist? New proof moves closer to an answer
#18I'm not trying to be flippant, although it may come off that way: why does any of this matter?
It’s interesting, and fun.
Most modern pure math is done completely independent of and without regard to applications(if it were, it would be ‘applied math’).
Re: How many real numbers exist? New proof moves closer to an answer
#19Earlier quoted context omitted.
It took many years to understand that! It’s not a flippant question at all. The answer is, it doesn’t matter. And that’s the joy of it. It wasn’t until I got into ML that I learned the value of doing unimportant work. When you’re free to think about inconsequential matters very seriously, you end up discovering so many useful things. It was how I independently rediscovered what is apparently called the Discrete Hartl…
> it doesn’t matter It doesn't matter yet . Applications of pure math happen downstream decades or centuries later. It's hard to predict the impact.
I don’t like this framing because it implies any piece of pure math becoming useful is just a matter of time, and I see no reason to suspect this is the case.
Re: How many real numbers exist? New proof moves closer to an answer
#20I'm not trying to be flippant, although it may come off that way: why does any of this matter?
We know that the cardinality of the natural numbers is less than the cardinality of the real numbers. The Continuum Hypothesis, which is a long unsolved problem, states that there are no sets with cardinality between the two. The posted article states that this new result strengthens the case against the hypothesis, that is that’s it’s probably false.
All of this is nuanced but is important to mathematics and philosophy.