Science

tama

(9,137 posts)

31. Not much point

Sat Apr 7, 2012, 03:05 PM

Apr 2012

fighting against Gödel:

"My thing is that a number has to have a finite definition somewhere, and those systems of representation where a number has a precise and finite definition is where it belongs."

Definition of number is a set of axioms creating a number theory, and Gödel proved that any logical system containing number theory (or rather just primes) does not reduce to a finite set of axioms. And as for primes, the notion is not limited to ordinality or cardinality, but just "one" and "self".

Here's an interview that I liked reading very much: http://www.urbanomic.com/Publications/Collapse-1/PDFs/C1_Matthew_Watkins.pdf

That's where I heard about 'Beurling’s Generalized Primes' first time.

Edit history

Please sign in to view edit histories.

Recommendations

0 members have recommended this reply (displayed in chronological order):

44 replies

= new reply since forum marked as read

Highlight:

If you're having math problems, I feel bad for you, son... [View all] tridim Mar 2012 OP

R&K for the first math post I've seen on DU longship Mar 2012 #1

Question for math teacher - Please. At the end of the year I have 100,000 Pesos... wake.up.america Feb 2013 #43

Well, it doesn't come out even. longship Feb 2013 #44

I disagree. Is PI a rational number? napoleon_in_rags Mar 2012 #2

Woot! for critical thinking and logic! TalkingDog Mar 2012 #3

A set of numbers is countable if it has the same cardinality as some subset of the natural numbers. Jim__ Mar 2012 #4

"there do not exist 2 integers, say n and m, such that pi can be written as n/m" napoleon_in_rags Mar 2012 #5

"... you know Z plus all integers of infinite length would probably have the same cardinality as R." Jim__ Mar 2012 #7

+! Hawkowl Mar 2012 #8

I will make it simpler for you. napoleon_in_rags Mar 2012 #9

"God created the integers" one_true_leroy Mar 2012 #10

This is a teachable moment. napoleon_in_rags Mar 2012 #11

A few points... one_true_leroy Mar 2012 #13

Yes, I've always had something of a flirtation with limits... napoleon_in_rags Mar 2012 #15

Had to jump in on this thread... Joseph8th Apr 2012 #22

As simply as it can be put, your statement is in direct contradiction to a Zermelo-Fraenkel axiom. Jim__ Mar 2012 #12

Awwwww hell..... one_true_leroy Mar 2012 #14

HELL yeah! I love it... Joseph8th Apr 2012 #23

Ah, my friend. You have forgotten your transfinite cardinals! napoleon_in_rags Mar 2012 #16

Guess again. Jim__ Mar 2012 #17

So you're saying 1+1+1...infinity is an integer? napoleon_in_rags Mar 2012 #18

The Axiom of Infinity says that 1 + 1 + 1 + 1 ... is an integer. Jim__ Apr 2012 #19

Yeah, it guarantees the size N is infinite, not that any number in N is infinite. napoleon_in_rags Apr 2012 #20

See post #4. Jim__ Apr 2012 #21

Nicely said... and... Joseph8th Apr 2012 #24

Now there's some interesting stuff. napoleon_in_rags Apr 2012 #26

Wellll.... Joseph8th Apr 2012 #27

But then pi's special in its relationship... Joseph8th Apr 2012 #28

Euler's identity tama Apr 2012 #30

Just answer me one question Joseph8th. napoleon_in_rags Apr 2012 #32

You're on an interesting track tama Apr 2012 #33

You're awesome Tama. napoleon_in_rags Apr 2012 #34

Mersenne primes tama Apr 2012 #35

God is Alive, Magic is Afoot. napoleon_in_rags Apr 2012 #36

Category theory tama Apr 2012 #37

I'm just incredibly glad to hear these people seeing the holes in set theory. napoleon_in_rags Apr 2012 #39

Not quite. Dr. Strange Apr 2012 #38

.999... is not equal to 1. napoleon_in_rags Apr 2012 #40

The problem is you can't treat infinity like a real number. Dr. Strange Apr 2012 #41

Agreed, that is the problem, but for both of us. napoleon_in_rags Apr 2012 #42

Not much point tama Apr 2012 #31

Transcendentals are strange tama Mar 2012 #6

Da! Transcendentals are strange... Joseph8th Apr 2012 #25

Deep shit ;) tama Apr 2012 #29