Posted on 01/12/2019 5:15:03 AM PST by BenLurkin
The trouble is, math is sort of broken. It's been broken since 1931, when the logician Kurt Gödel published his famous incompleteness theorems. They showed that in any mathematical system, there are certain questions that cannot be answered. They're not really difficult they're unknowable. Mathematicians learned that their ability to understand the universe was fundamentally limited. Gödel and another mathematician named Paul Cohen found an example: the continuum hypothesis.
The continuum hypothesis goes like this: Mathematicians already know that there are infinities of different sizes. For instance, there are infinitely many integers (numbers like 1, 2, 3, 4, 5 and so on); and there are infinitely many real numbers (which include numbers like 1, 2, 3 and so on, but they also include numbers like 1.8 and 5,222.7 and pi). But even though there are infinitely many integers and infinitely many real numbers, there are clearly more real numbers than there are integers. Which raises the question, are there any infinities larger than the set of integers but smaller than the set of real numbers? The continuum hypothesis says, yes, there are.
Gödel and Cohen showed that it's impossible to prove that the continuum hypothesis is right, but also it's impossible to prove that it's wrong. "Is the continuum hypothesis true?" is a question without an answer.
In a paper published Monday, Jan. 7, in the journal Nature Machine Intelligence, the researchers showed that EMX is inextricably linked to the continuum hypothesis. It turns out that EMX can solve a problem only if the continuum hypothesis is true. But if it's not true, EMX can't.. That means that the question, "Can EMX learn to solve this problem?"has an answer as unknowable as the continuum hypothesis itself.
(Excerpt) Read more at livescience.com ...
In my case, the more irrelevant the printed thing is, the more the idiot will whine about it.
Taking a stand alone printer away from some of my users when they die is almost taking the first born based on the crying.
Pi as a fraction is a real number not an approximation. Pi as a decimal is an irrational number and goes on infinitely, I think. If the above is true it might have to do with the mechanics of the number system we use, but I do not know how that could be.
QED
Long term ratio of a Fibonacci sequence.
1.618...
Does using a larger infinity in solving an integral make it more accurate?
I’m sticking with the “One Size Fits All, Infinity”.
Hillary was Right!
Math is Hard.
I spent a year reading Godel one day.
There aren’t more real numbers than integers because both lists are endless. Infinity is not a number, it means ‘endless’.
Known Knowns - Educated, I know what I know when I know it.
Known Unknowns - Scholarly research and study, I don't have the answer yet, but still thinking and looking for it.
Unknown Unknown - Village Idiot level of ignorance. (Democrat)
Maybe not. If one can get enough taxpayer $$$'s then one can spend a lifetime trying! It beats watching the sex life of some toad.
Touché- maybe just not my cup of tea.
As soon as one blurs the distinction between continuous and discrete quantities having a coherent discussion about what infinity means becomes meaningless.
Infinity with regard to discrete quantities means that there is never a greatest, you can always add one.
Infinity with regard to continuous quantity means you can divide it in any manner you please.
In computer science the distinction between continuous and discrete quantity has been for the most part preserved.
In modern “pure” mathematics the distinction has been obscured. This causes modern mathematics to become a grotesque exercise. Anyone who has endured a graduate level course in “real analysis” can attest to the stupid proofs that claim that the real number system can be constructed, it is absurd.
You can trace this back to Nicholas Bourbaki, aka the mathematicians that Hitler chased out of Germany. Hitler was a monster, but he was right about the corruption of mathematics.
The premise is that numbers are a real thing, rather than a human construct to keep accounts in approaching an unknowable reality.
This thread explains why I hate the idea of self driving cars
Very qualified as an engineer. And I can prove it because I do not know how to spell Daisies.
Married an artist. She taught me how to appreciate the other side.
I miss watching Donald Rumsfeld chop off the heads of ignorant reporters.
Integers are countably infinite, real numbers are uncountably infinite. They are provably different, e.g. by Cantor’s diagonal proof. The number of rational numbers is also countable.
I have a proof for this, but theres insufficient space to show it here.”
Thank you Monsieur Fermat
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