Mathematicians Measure Infinities and Find They’re Equal

[battletoad]

In a breakthrough that disproves decades of conventional wisdom, two mathematicians have shown that two different variants of infinity are actually the same size. The advance touches on one of the most famous and intractable problems in mathematics: whether there exist infinities between the infinite size of the natural numbers and the larger infinite size of the real numbers.

The problem was first identified over a century ago. At the time, mathematicians knew that “the real numbers are bigger than the natural numbers, but not how much bigger. Is it the next biggest size, or is there a size in between?” said Maryanthe Malliaris of the University of Chicago, co-author of the new work along with Saharon Shelah of the Hebrew University of Jerusalem and Rutgers University.

In their new work, Malliaris and Shelah resolve a related 70-year-old question about whether one infinity (call it p) is smaller than another infinity (call it t). They proved the two are in fact equal, much to the surprise of mathematicians.

“It was certainly my opinion, and the general opinion, that p should be less than t,” Shelah said.

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Quite a surprising result!

 

[ScottulusMaximus]

MY BRAIN!!!! IT HURTS!!!

So far beyond my understanding it's not funny.

 

[Arthur]

Astonishing. All my adult life I've been under the impression that all infinities are equally infinite. Can't imagine why some mathematicians thought otherwise.

 

[Ninja'd]

 

[UrBaN963]

So something that is without scope, is equal to something without scope? Well shucks Barb, that done messed my brain right up!

 

[etienne_marais]

From what I remember, prior to this, the conventional infinity magnitude orders were mathematically determined by mappings but only had theoretical/'philosophical' application, i.e. not used in actual calculations. Does anybody have it otherwise, i.e. will any mathematical application outside the realm of 'mathematical philosophy' be affected by this ?

 

[ScottulusMaximus]

Astonishing. All my adult life I've been under the impression that all infinities are equally infinite. Can't imagine why some mathematicians thought otherwise.

So something that is without scope, is equal to something without scope? Well shucks Barb, that done messed my brain right up!

They didn't prove all infinities are equal, just that p and t are equal.

 

[Batista]

From what I remember, prior to this, the conventional infinity magnitude orders were mathematically determined by mappings but only had theoretical/'philosophical' application, i.e. not used in actual calculations. Does anybody have it otherwise, i.e. will any mathematical application outside the realm of 'mathematical philosophy' be affected by this ?

Heard of Space and Time?

We are not meant to understand this just as yet.I do see it having an impact in the far future (200-300 years from now) based on this :

https://www.alumni.cam.ac.uk/news/beyond-number-the-role-of-infinity-in-understanding-the-universe

 

[spiderz]

Did they remember to carry the 1?

 

[TehStranger]

Interesting, and just the other day I watched this video on how to count past infinity. https://m.youtube.com/watch?feature=youtu.be&v=SrU9YDoXE88

Worth the time if you've got 20 minutes to set your brain on fire.

 

[konfab]

From what I remember, prior to this, the conventional infinity magnitude orders were mathematically determined by mappings but only had theoretical/'philosophical' application, i.e. not used in actual calculations. Does anybody have it otherwise, i.e. will any mathematical application outside the realm of 'mathematical philosophy' be affected by this ?

String theory uses weird sets of infinity, so it could be impacted.

 

[konfab]

From what I remember, prior to this, the conventional infinity magnitude orders were mathematically determined by mappings but only had theoretical/'philosophical' application, i.e. not used in actual calculations. Does anybody have it otherwise, i.e. will any mathematical application outside the realm of 'mathematical philosophy' be affected by this ?

String theory uses weird sets of infinity, so it could be impacted.

 

[Ninja'd]

String theory uses weird sets of infinity, so it could be impacted.

String theory uses weird sets of infinity, so it could be impacted.

konfab duplicates to infinity which in this case is very low

 

[Arthur]

They didn't prove all infinities are equal, just that p and t are equal.

Indeed. We should get there by end of the century.

 

[Splinter]

Indeed. We should get there by end of the century.

Only after AI's take over and replace us.

 

[Thor]

One heck of a way to het to that amswer

 

[Aquila ka Hecate]

One heck of a way to het to that amswer

Why, how would you have done it?