Godel's Incompleteness Theorem

[lini...]

The Nature of Belief--Gary Miller uses Godel's incompleteness theorems to prove the necessity for GOD



transcript:
http://www.lecture-transcripts.com/2010/01/islam-nature-of-belief.html

 

[blackzeus]

The Nature of Belief--Gary Miller uses Godel's incompleteness theorems to prove the necessity for GOD

Somebody who gets it. Nikkaz are breaking their proverbial mental backs using mathspeak while missing the essence of Godell's theorem. Logically, since everything is created by design, there must be somebody who has all the answers. Since AT THE BASIS of his reasoning man doesn't have all the answers (as proven by Godell's incompleteness theorem), there must be somebody that does, after all, anything made by design has a designer. Now folks, who is that Somebody?

 

[69 others]

man what the f*ck @manwhatthefukk , no, once you plug in really large numbers its wrong, that's what the (x,y) plot shows. There is no end, it goes to infinity, so in essence:

0+1+...+ = (infinity*(infinity+1)/2 = (approximately) infinity*infinity/2 or infinity^2/2. Let's make subsets the of the lower and upper limit of the set to make it easier for you to understand my point.

Let's describe the upper subset (1,000,000,000=T)as {...,T,T+1,T+2}, and the lower subset as {0,1,2,3,4}. For the lower subset there's no problem. 4*(4+1)/2= 10 which is close to 4^2/2= 8. Now for the upper subset (T*(T+1))/2 = 5.000000005e17 (17 0's). T^2/2= 5e17 (17 0's). T^2 = 1e18 (18 0's). In other words, you dividing a T^2/2 = T^2-5e1. IIf it's already that little of a difference at a trillion, at infinity, the difference between n^2/2 and n^2 is truly negligible. So essentially, the bigger the number gets, the smaller the difference between n*(n+1)/2 and n^2. So once you get to really large numbers, you are saying basically that 0+1+2...+infinity+infinity+1 = infinity^2, which is why the x,y plot never approaches a finite number (e.g. divergent), because that's not true. Think about it man, 10*10 = 10+....+10 ten times. so how many MORE times would you have to add infinity on itself for it to equal infinity squared? And on top of it, you are decreasing the number you are adding by each time. That would be like you expecting 10+9+8+7+...=10^2, that's crazy talk. As the axiom approaches infinity, the math behind it becomes ludicrous. You believe it's true at infinity by faith, not by fact. That is Godell's point.

nah breh sorry. i think you misunderstanding some things here especially with the chart, infinity, and axioms.

let's start with the prove.

so you've heard or seen in text books that the sum integers from one to n is equal to (n^2 + n) / 2. to prove we use mathematical induction which theorem generally states that for a subset S of N (natural numbers) of all positive integers satisfying properties: a) 1 is in S b) for all n in N, n is in S then n + 1 is in S then S = N

so then we proceed:
1) 1 = (1 * (1 + 1) )/ 2 we could try a few more numbers (2,3,4,5,6) which we'll see is true also. so let all those numbers we see satisfy the equation be in the set S even though we see by the theorem it's suffecient to only show that 1 is in S.
2) now for part b of the theorem. let's "assume" (the induction hypothesis) that 1 + 2 + ....+ n = n*(n+1)/2.
3) we make use of the induction hypothesis and you know the rest. if resulting equation are equal then you proved your point if not then it's not.

if you proved that this is infact true then for any number n whether it's one, a billion, a zillion, or whatever Natural number this is true. i'm not sure what you're doing with your arithmetic and your infinities but it doesn't make sense.


for a more concrete example run this code


also let's cut the nonsense. when it comes to the incompleteness theorem your talking out your ass and you're trying to wiki and google your way through this. this suppose to be higher learning what you don't know you don't let's stop with the fronting to boost egos and save face

 

[blackzeus]

nah breh sorry. i think you misunderstanding some things here especially with the chart, infinity, and axioms.

let's start with the prove.

so you've heard or seen in text books that the sum integers from one to n is equal to (n^2 + n) / 2. to prove we use mathematical induction which theorem generally states that for a subset S of N (natural numbers) of all positive integers satisfying properties: a) 1 is in S b) for all n in N, n is in S then n + 1 is in S then S = N

so then we proceed:
1) 1 = (1 * (1 + 1) )/ 2 we could try a few more numbers (2,3,4,5,6) which we'll see is true also. so let all those numbers we see satisfy the equation be in the set S even though we see by the theorem it's suffecient to only show that 1 is in S.
2) now for part b of the theorem. let's "assume" (the induction hypothesis) that 1 + 2 + ....+ n = n*(n+1)/2.
3) we make use of the induction hypothesis and you know the rest. if resulting equation are equal then you proved your point if not then it's not.

if you proved that this is infact true then for any number n whether it's one, a billion, a zillion, or whatever Natural number this is true. i'm not sure what you're doing with your arithmetic and your infinities but it doesn't make sense.


for a more concrete example run this code

http://en.wikipedia.org/wiki/Divergent_series

In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.

I am at y'all. To put it layman's terms, divergence would be like a+b = infinity. There should never be an instance where two natural numbers are not equal to another natural number. Any summation series over the entire set of natural numbers that at any point doesn't have a finite limit is divergent, f*cked up, inconsistent, incomplete, WRONG. So what was solution created by the Council of the High Math Priests? (

):

http://en.wikipedia.org/wiki/Divergent_series#Theorems_on_methods_for_summing_divergent_series

Summation methods usually concentrate on the sequence of partial sums of the series. While this sequence does not converge, we may often find that when we take an average of larger and larger initial terms of the sequence, the average converges, and we can use this average instead of a limit to evaluate the sum of the series

So basically, we take something we can't understand, and try to explain it in a way we can comprehend. What does that sound like? Me personally, I like to light some incense and energize my chakras before I use my calculator, what about you?

 

[OCCAMS_RAZOR]

Step #1: Construct a predicate

Step #2: Prove that the predicate is true on the basis

Step#3: Induction Hypothesis (assume that the predicate is true for n P(n))

Step#4: Prove that P(n+1) is true

n can be any real #. where does faith factor into all of this?

 

[blackzeus]

Step #1: Construct a predicate

Step #2: Prove that the predicate is true on the basis

Step#3: Induction Hypothesis (assume that the predicate is true for n P(n))

Step#4: Prove that P(n+1) is true

n can be any real #. where does faith factor into all of this?

Master @OCCAMS_RAZOR, of the Council of the High Priests of Math, this is worshipful math servant @blackzeus.

I have a question Master. Please explain the difference between step 2 and 3, and me saying that because an object as simple as a car obviously has a designer, logically the intergalactic system which is infinitely more complicated has one as well. Are not both in essence a leap of faith based on a logical premise?

 

[OCCAMS_RAZOR]

but it is true. it's not a groundless assumption as we proved that the predicate is true on the basis. if n = basis, and P(n) is true, and we've proven that P(n) -> P(n+1) then we're not just pulling assumptions out of our ass. it's a very rigorous proof. from my perspective there's nothing about this that seems flawed or non-rigorous.

 

[69 others]

http://en.wikipedia.org/wiki/Divergent_series



I am at y'all. To put it layman's terms, divergence would be like a+b = infinity. There should never be an instance where two natural numbers are not equal to another natural number. Any summation series over the entire set of natural numbers that at any point doesn't have a finite limit is divergent, f*cked up, inconsistent, incomplete, WRONG. So what was solution created by the Council of the High Math Priests? (

):

http://en.wikipedia.org/wiki/Divergent_series#Theorems_on_methods_for_summing_divergent_series



So basically, we take something we can't understand, and try to explain it in a way we can comprehend. What does that sound like? Me personally, I like to light some incense and energize my chakras before I use my calculator, what about you?

breh it's all love but you don't know what the hell you're talking about stop googling shyt you barely understand and trying to pass it off as your own understanding when you barely understand it. the set of natural numbers is infinite (well countable infinite) if that's what have you confused

 

[blackzeus]

but it is true. it's not a groundless assumption as we proved that the predicate is true on the basis. if n = basis, and P(n) is true, and we've proven that P(n) -> P(n+1) then we're not just pulling assumptions out of our ass. it's a very rigorous proof. from my perspective there's nothing about this that seems flawed or non-rigorous.

Master @OCCAMS_RAZOR, of the Council of the High Priests of Math, this is worshipful math servant @blackzeus.

I have a question Master. Are the following not the correction definition of the word assumption?:

http://dictionary.reference.com/browse/assumption

1.
something taken for granted; a supposition: a correct assumption. Synonyms: presupposition; hypothesis, conjecture, guess, postulate, theory.
2.
the act of taking for granted or supposing. Synonyms: presumption; presupposition.
3.
the act of taking to or upon oneself. Synonyms: acceptance, shouldering.
4.
the act of taking possession of something: the assumption of power. Synonyms: seizure, appropriation, usurpation, arrogation.
5.
arrogance; presumption. Synonyms: presumptuousness; effrontery, forwardness, gall.

What is the essential difference our High Priests assuming the predicate is true on the basis, and other religions assuming the predicate is true on the basis?

Faith of Math:
A^2+B^2=C^2; 1^2+1^2+1^2 = 1; let's assume it's true for all elements in the set of natual numbers

Faith by Intelligent Design:
All creation is made by intelligent design; computers are all made by intelligent design; let's assume all creations more complicated than computers (any existing organism) are also made by intelligent design

Please Master @OCCAMS_RAZOR, please explain to your lowly worshipful math servant the difference.

Spoiler

Please note I am not trying to diss you personally, I imagine Godell looking his colleagues like the every time his theory was read , and just trying to recapture the essence of that in hopes you guys get the essence of Godell's theory.

 

[blackzeus]

breh it's all love but you don't know what the hell you're talking about stop googling shyt you barely understand and trying to pass it off as your own understanding when you barely understand it. the set of natural numbers is infinite (well countable infinite) if that's what have you confused

Ad hominem, I expect better from an educated man like you. Let me know when your calculator solves 1/0

Spoiler

No disrespect of course Master @manwhatthefukk of the High Council of Math Priests

 

[OCCAMS_RAZOR]

Master @OCCAMS_RAZOR, of the Council of the High Priests of Math, this is worshipful math servant @blackzeus.

I have a question Master. Are the following not the correction definition of the word assumption?:

http://dictionary.reference.com/browse/assumption



What is the essential difference our High Priests assuming the predicate is true on the basis, and other religions assuming the predicate is true on the basis?

Faith of Math:
A^2+B^2=C^2; 1^2+1^2+1^2 = 1; let's assume it's true for all elements in the set of natual numbers

Faith by Intelligent Design:
All creation is made by intelligent design; computers are all made by intelligent design; let's assume all creations more complicated than computers (any existing organism) are also made by intelligent design

Please Master @OCCAMS_RAZOR, please explain to your lowly worshipful math servant the difference.

Spoiler

Please note I am not trying to diss you personally, I imagine Godell looking his colleagues like the every time his theory was read , and just trying to recapture the essence of that in hopes you guys get the essence of Godell's theory.

it's not an assumption. 'assume' was merely used to construct a general solution. the critical thing is that i can show that P(n) implies P(n+1). once that is done i can throw all assumptions out the window and SHOW you P(1) -> P(2) -> P(3) -> .... -> P(whatever number you like)

I'm not disputing the fact that godel's theory shook the very foundations of mathematics i simply think that you using induction to illustrate the theory's applicability is wanting.

 

[blackzeus]

it's not an assumption. 'assume' was merely used to construct a general solution. the critical thing is that i can show that P(n) implies P(n+1). once that is done i can throw all assumptions out the window and SHOW you P(1) -> P(2) -> P(3) -> .... -> P(whatever number you like)

I'm not disputing the fact that godel's theory shook the very foundations of mathematics i simply think that you using induction to illustrate the theory's applicability is wanting.

Then why does Euclidean algorithim for integer division not include 0? Is 0 not an integer in the set of all natural numbers? Has the Faith of Math failed us yet again?

Spoiler

<------This is Godell mocking you, not me breh

 

[OCCAMS_RAZOR]

Then why does Euclidean algorithim for integer division not include 0? Is 0 not an integer in the set of all natural numbers? Has the Faith of Math failed us yet again?

Spoiler

<------This is Godell mocking you, not me breh

as i understand, mathematicians decided this arbitrarily to fill in a gap in the logic. same reason why they also decided that 1/0 should be undefined, or why complex and 'imaginary' numbers were invented.

i think i'm starting to see what you're trying to say. but that whole yarn you were spinning about induction. nah bruh. that's not cutting it.

 

[DANKTHRONE]

Godel was also a paranoid schizophrenic so I can't take his views on religion seriously

 

[blackzeus]

]as i understand, mathematicians decided this arbitrarily to fill in a gap in the logic. same reason why they also decided that 1/0 should be undefined, or why complex and 'imaginary' numbers were invented.

Hmm, arbitrarily filling in gaps in logic now are we? I wonder what other set of beliefs does something similar?

i think i'm starting to see what you're trying to say.

but that whole yarn you were spinning about induction. nah bruh. that's not cutting it.

et tu quoque?