# Can math prove things with 100% certainty?

Author: Math_Enthusiast

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a = 1, b = 1

(a-b)(a+b) = 0
(a-b)(a+b)/(a-b) = 0/(a-b)
1(a+b) = 0
(a+b) = 0
1 + 1 = 0 (Hence, 1+1 not equal to 2). Thoughts?

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@Slainte
Except that: a = 1, b = 1

1(a+b) = 2
(a+b) = 2
1 + 1 = 2

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You are the final word, I wont debate you on it. I've already debated it and been proven wrong using mathematical semantics. 1.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 is not 2

Just one question is 1.899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 the same as 1.9 since 1.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999 is the same as 2?
Yes
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@Sidewalker
Let's denote x = 1.999... and multiply both sides of the equation by 10: (you can actually pick any number)

10x = 19.999...

Now, subtract x from both sides:10x - x = 19.999... - 1.999...9x = 18
Divide both sides by 9:x = 2
So, mathematically, we can conclude that 1.999... is equal to 2.
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@Slainte
Since you have to include the caveat that (a-b) cannot equal zero (division by zero error) then the proof fails.

Maybe use different numbers?
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1.9 = 2
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@Math_Enthusiast
1 triangle  /\  + 1 triangle /\  = 4 triangles \Y/ and 12 angles when synrgetically applied = the four surface triangles of a tetrahedron \Y/

4 * 12  ---60 degree angles---  = 720 degrees  and 720 degrees = 2 circles = one tetrahedron

Now we have two sets of Pi ergo, Pi + Pi =  6.28 31 85 30 7 1 7 95 864 7 69 25 286 7 66 55 9 { one tetra set of 12 surface angles }

one tetra set of 12 angles to 2nd power = 39.4 7 841 7 60 435 7 43 44 7 533 7 96 39 99 50 5

one tetra set of 12 angles, plus Pi = 42.62 00 10 25 7 94 7 22 7 7 13 80 060 7 382 7 84
...note: 42 is Hitchhikers guides great computer answer to everything

2} one tetra set of 12 angles to 3rd power = 248.05 02 13 44 23 98 56 14 03 81 05 20 53 68 1
...note: there are no #7's in that resultant

7 is combination of structural  integrity  three-ness and systemic integrity as four-ness

Heptagon is first polygon with irrational interior surface angle 128.57 and the 7 of them total to 899.99 or 900.

900 is a whole lot of structural integrity as threen-ess. 900 / 3 = 300

However, the 12, 60 degree angles of tetrahedron = 720 degrees, so shall we compare 2D heptagon's 900 degrees to 3D tetrahedron's 720 degrees?

2D, 900 minus 3D, 720 = 180 degrees. H,mm 180 degrees makes me think of the diameter of a circle --aka two radii-- or as one half of circle and one half of Pi?

Pi / 2 = 1.5 7 0 7 96 326 7 94 89 66 19 23 13 21 69 1 63 98
..note: so this value is the half a Pi ergo half a circle in relation too the diameter of the circle? H,mm

Not sure where any of this would lead. First time Ive ever done this calculations before. kinda link comparing oranges and apples?

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@Math_Enthusiast
“Generally accepted”, as opposed to “universal or absolute” acceptance, which is to say the definition is not accepted with100% certainty.
Definitions are arbitrary anyway, so I'm not sure why this is a point of contention. The point is that 1 + 1 = 2 is known with 100% certainty for the objects that most mathematicians use the symbols 1 and 2 to describe.
It’s not a point of contention, as faras I can tell you are contending with my original response by agreeing with it.The subject matter was “Can math prove things with 100% certainty?”, epistemicallyspeaking, the answer is no, but you can achieve certainty by definition withina formal system, 100% certainty requires 100% agreement on the definitions. Youare saying “generally” and “most mathematicians”, which doesn’t translate into100% certainty.  Any mathematical proofrelies on a structure of logic and a an acceptance of axioms, neither of whichtranslates into total agreement or 100% certainty.

Yep, “Certainty in a formal system isa matter of definition”.   BTW, I’m 100% certain Sherlock Holmessmoked a pipe.
I'm not sure what your point is.
I get that alot, probably because a lot of my posts include inside jokes that are just between me and me.

The first sentence was quoting myinitial post to point out your contention by agreement, the second sentencealludes to a common statement in the philosophy of mathematics regardingwhether or not you can have objective knowledge about mathematical objects. Ifmathematical objects only exist in a Platonic realm, and not in the real world,then how can there be certain knowledge about them.  Philosophers like to point out that despite SherlockHolmes being a fictional character, as a construct that doesn’t exist in thereal world, it is still a true statement that he smokes a pipe.  I thought that’s where you were going with thecomment about objectivity.

It took Russell and Whitehead 360pages to define and give meaning to the terms “1”, “+”, “=”, “2” and to lay thelogical foundation from which they could consider 1+1=2 to be proven.  They couldn’t have been more tedious, andwent off on a lot of tangents, apparently they themselves didn’t believe theywere there until page 362, I think most mathematicians think they hadn’t adequately defined "addition" yet, many believe it as actually took them 379 pages.
Exactly. The proof that 1 + 1 = 2 was rather short, it's just that prior to that things like "1" and "2" weren't even defined yet.

Then ZFC and Godel came along andsquashed Logicism like a bug.
Did they? I'm not sure why there are so many misconceptions about Gödel's incompleteness theorem. All it says is that in any formal system F which contains basic arithmetic, there exists a statement A such that neither A nor its negation is a theorem in F. That's it. It doesn't mean that math is broken or anything like that. Math studies theorems and their proofs, most commonly within ZFC, but also within PA and other formal systems, and is in turn merely an extension of basic logic.
Hilbert, Frege, and Russell all sawthe significance of Godel’s theorem, Hilbert certainly wasn’t happy about it,but he recognized that it put a bullet between the eyes of his Formalism aswell as Frege and Russel’s Logicism.  Thepurpose of the Principia was to prove that mathematics could be proved usingLogic, ZFC crushed Russell’s type theory and  Godel’s theorem was effectively a proof that Logicismwas not possible.   Hilbert’s Formalism required a proofthat it was consistent and complete, Godel’s proof demonstrated that no axiomatic system couldbe both consistent and complete, Hilbert begrudgingly cancelled his Formalism efforts in response to Godel incompleteness.

I owe, I owe, it's off to work I go...this issue keeps coming up between you and I, when I have some time how about I do a post about my read of the historical foundations of mathamatics, the fact that it's "broken" hasn't slowed Mathematics down one bit, but I will make an argument that it really is "broken".

No. What?
LOL, just messing with you a little bit, I was alluding to, in myopinion, that your 1+1=2 proof is practically a redundancy to the ZFC axion ofunion.

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@Greyparrot
Let's denote x = 1.999... and multiply both sides of the equation by 10: (you can actually pick any number)

10x = 19.999...

Now, subtract x from both sides:10x - x = 19.999... - 1.999...9x = 18
Divide both sides by 9:x = 2
So, mathematically, we can conclude that 1.999... is equal to 2.
2 divided by 6 equals a third, a third times 6 equals 2

2 divided by 6 = .33333 repeating
6 times .33333 repeating is 1.9999 repeating.
2=1.999 repeating.
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@Sidewalker
Yeah, there are multiple ways to show this.

Your way is less formal and much easier to understand.
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@Greyparrot
Yeah, there are multiple ways to show this.
Your way is less formal and much easier to understand.
It's not that hard to understand, but for some mysterious reason, there are about a billion internet debates arguing that .9999 repeating doesn't equal 1.

I think all you have to do is throw the word "infinite" into a post and people lose their minds.

It's why Georg Cantor died in an insane asylum.
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@Sidewalker
"I think all you have to do is throw the word "infinite" into a post and people lose their minds."

Its either completely  and willfully ignored. Or deemed irrelevant with regard to fractional numbers. "Close enough"

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1 triangle  /\  + 1 triangle /\  = 4 triangles \Y/ { as tetrahedron ergo 12 surface angles} when applied synergetically via  LINK

1 + 1 = 4 and 3 + 3 = 12 synergetically. Old news

4 * 12  ---60 degree angles---  = 720 degrees  and 720 degrees = 2 circles = one tetrahedron

One circle = Pi + one circle = Pi and two circles of Pi total = 6.28 31 85307179586476925286766559

So a tetrahedron --has 6 chords/edges/vectors--- translates as 6.28 31 85 30 7 19 58 64 7 69 25 286 7 66 55 9

H,mm the 6 vectorial chords is close to the Pi/tetrahedron's 6.28 { rounds to 6.3 }

So the minimal circle { 2D enclosure } is a triangle, however, we can see from the above to get two circles { 720 degrees } we need the four surface triangles of the tetrahedron i.e. it takes two triangles to equal one curved circle.

So two Euclidean triangles { /\  /\ } are equal too one Riemann curved circle { O }.  Ok, now we begin to grasp the differrence between a curved convex/positive space and a Euclidean { non-curved space }.

There also other ways we see this differrence of Euclidean vs Riemann positive curvature. With the curved sphere 120 right-tringles that Fuller used to discover his right-triangle data of his gegodesic domes.  902.33 LINK

And in the cubo-octahedron/vector equlilbrium we see how Archimedes disccovered that a curved VE/cubo-octahedron, had a outer surface area that was equal to the four, bisecting hexagonal planes that, define the VE/cubo-octahedron.  Whereas with the Euclidean VE, the surface is slightly less.

..."The holographic principle states that the entropy of ordinary mass (not just black holes) is also proportional to surface area and not volume; that volume itself is illusory and the universe is really a hologram which is isomorphic to the information "inscribed" on the surface of its boundary"....

So we have the four bisecting plane areas of VE being equal to the curved outer surface { thank you Archimedes }.

.."Hawking's calculation fixed the constant of proportionality at 1/4; the entropy of a black hole is one quarter its horizon area in Planck units"...

So R Penrose proved Einstiens Gravitaional singularities within context of a black hole aka null geodesics or ' geodesic incompleteness'.

Hawking did the same for Universe in total  Infinite density as prior to the Big Bang.

So when is math incorrect? When its answers are infinite magnitude.

..."This suggests that matter itself cannot be subdivided infinitely many times and there must be an ultimate level of fundamental particles. As the degrees of freedom of a particle are the product of all the degrees of freedom of its sub-particles, were a particle to have infinite subdivisions into lower-level particles, the degrees of freedom of the original particle would be infinite, violating the maximal limit of entropy density. The holographic principle thus implies that the subdivisions must stop at some level"...

Again, look at this LINE of a tetrahedron going to zero volume while maintaining its four planes, out side the surface of the VE as black hole equilibrium.  It is  not ever in equilibrium, because of entropy-syntropy. Because of Gravity-Dark Energy.  Because of what goes in must come out again and what goes out must come in again.

Infinite = lack of structural and systemic integrity  --no closure-

Finite = structural and systemic integrity --closure--- Triangle/circle/spiral around and around and around.

There is not gravity well, there is Gravity-dark Energy spirals around, that come closer together and never infinite because they have always been and always will be a finite set of overlapping and interfering Quantum Space-time tori.

The abstract numbers exist as the underlying sequence of order, that, always come around to meet themselves withing context of each finite set of overlapping, Quantum Space-time Tori. When the math says infinite, then the math is incorrect ergo the invention of re-normalization.

..."The field of “renormalization theory” emerged from a crisis in physics in the early 20th century, when physicists realized that this change of constants can produce infinite results in the case of quantum field theory, at the time considered to be the ultimate framework for the laws of nature at a microscopic scale. The problem was solved by a new technique (renormalization) by which the summation of an infinite number of energy levels at short distances was avoided by imposing a minimum cutoff on fields.

.......Shinichiro Tomonaga, a Nobel prize-winning physicist who joined RIKEN's Nishina Laboratory in 1932, played a seminal role in the development of renormalization theory. The son of a professor of philosophy at Kyoto Imperial University, Tomonaga worked on research in the area of quantum electrodynamics under the guidance of Yoshio Nishina.

.....In 1943, he published the “super-many-time theory,” which reconciled quantum mechanics with the theory of relativity. Tomonaga further developed these ideas in his work on renormalization theory, for which he, along with Julian Schwinger and Richard Feynman, was awarded the Nobel Prize in 1965."...

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@Sidewalker
I have a question for you:

What is an objectively true statement but a statement which is true by definition?

Also, you continue to insist that because the definitions are not fully and universally agreed upon, that makes these results not "100% certain." When I claim that 1 + 1 = 2, I am making a claim about my definitions of 1 and 2, no more, no less. If someone else disagrees on what those definitions should be, then they don't actually disagree with me on the statement that I am asserting, but rather, they disagree with me on whether what I call 1 and 2 should be called 1 and 2. Those are two different kinds of disagreement.
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@Math_Enthusiast
I have a question for you:

What is an objectively true statement but a statement which is true by definition?
An objectively true statement is astatement about facts that can be confirmed independent of any subjective bias,under the correspondence theory of truth, it is a statement that corresponds toexternal reality. My car is blue, it is raining, the Earth revolves around thesun, these are objectively true statements because they can be verified empiricallyto correspond with external reality.
Also, you continue to insist that because the definitions are not fully and universally agreed upon, that makes these results not "100% certain." When I claim that 1 + 1 = 2, I am making a claim about my definitions of 1 and 2, no more, no less. If someone else disagrees on what those definitions should be, then they don't actually disagree with me on the statement that I am asserting, but rather, they disagree with me on whether what I call 1 and 2 should be called 1 and 2. Those are two different kinds of disagreement.
The topic was “Can math prove things with 100% certainty?”, andmy answer wasn’t all that hard to understand, “Certainty in a formal system isa matter of definition” and “100% certainty becomes a matter of 100% agreementon definitions”.  I don't know how to be more clear than that.

You seem to be making a claim about subjective truth here, youare confusing objective truth with subjective truth.  if someone disagrees on the definitions youare using, then they will disagree with the truth of your assertion, if theyagree on the definitions you are using, then they will agree with yourconclusions. Recognizing that your definitions yield your conclusions, is not somespecial kind of disagreement. Both cases are in agreement with my initial statement.

It sounds like you are contending with my point by agreeingwith it again.  If someone agrees with myassertion that certainty in a formal system is a matter of definition to theextent that there is agreement on definitions”, so it follows that they wouldrecognize that your definitions yield certain conclusions for you, and for someonewith different definitions there will be different conclusions.

I think you are trying to split hairs where there is no hair.
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There exists only five regular/symmetrical and convex polyhedra.  This is that has ever been seen and no others will ever be seen.

This aka eternal absolute cosmic principle aka absolute truth. The more we refine our definitive descriptions the closer we come to absolute truth. Until then we just orbit the absolute truth trying to get closer to it.

It is safe to say that, we are trapped by absolute.  So when some say, the truth will set you free, this is not always the case.

..'1] objectively observe and harvest the info,

..2} sort the info into catagories,

...3} winnow out patterns and principles from those catgories,

...4} subjectively apply those patterns and principles to technology  --and Meta-space maths---, that used to sustain the integrity of self, others, environment and Universe { @ }. '...para-phrasing bucky fuller, with some additions of my own.

All prime numbers fall on the following line, that pretend goes onward infinitely:

1...2p....3p....4....5p...6...7p...8....etc

Or we can say that, all prime numbers --except 2p and 3p-- fall only on the 2nd line --along with non-prime numbers--   in the following pattern:

...0.................................6................................12.................etc
.........1....................5p.......7p...................11p.......13p.........etc
...............2p........4....................8........10...............................etc
....................3p..............................9.......................................etc

From the latter set of above truths we can translate that into a 2D hexagon, with 6 radii, where we go around in a semi-spiral sequence, and all prime numbers ---except 2p and 3p--- fall only on two of the radii, that, are seperated by a single radii between them. In this pattern zero { 0 } is the nuclear { centered ]

............................................21...................................................20............................
.................................................15........................................14...................................
......................................................9..........................8..................................................
.........................................................3p............2p..........................................................
..................................16........10...........4........0..............1......7p.......13p.......19p etc....
..............................................................5p..........6........................................................
........................................................11p...................12................................................
..................................................17p...............................18..............................................
................................................etc.......................................etc........................................
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@Math_Enthusiast
Yes. Intriguing. I will give it some thought and come back to you.
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Can we inside out a number?  I dont think so as a number alone is not a area nor a voume, however, we can use negative numbers, and that may closelr resemble mirroring a number. Maybe not.

But we can inside out a semi-2D pattern of numbers ex. I take the previous symmetrical pattern I posted in #46, --bottom of this page---  and inside-out the top and bottom line, moved to the inside to create an asymmetrical pattern:

…1………………5p……7p……………11p……13p..inside now out at top
0………………………6………………………12…….top outer now inside
……………3p……………………9…………………...bottom outer now inside
………2p……4………………8……10………………..inside now out at bottom

Initial symmetrical pattern below as outside-out

...0.................................6................................12.................etc
.........1....................5p.......7p...................11p.......13p.........etc
...............2p........4....................8........10...............................etc
....................3p..............................9.......................................etc

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Sorry, I dont believe in math.
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However, if you try to prove something, you should at least make sure its not circular reasoning lol.

Sadly, all math is circular reasoning. Thats why I dont believe in it.
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@Best.Korea
However, if you try to prove something, you should at least make sure its not circular reasoning lol.

Sadly, all math is circular reasoning. Thats why I dont believe in it.
I know you’re trolling but I’m going to take you seriously to entertain myself.

Basic forms of math such as understanding the difference between 1 thing and 2 things have an evolutionary basis that give animals an advantage in how to navigate the world. Same applies to geometry, even more so. You can say you don’t believe in math, but that’s not how your biology works.
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@Reece101
Basic forms of math such as understanding the difference between 1 thing and 2 things have an evolutionary basis that give animals an advantage in how to navigate the world.
So "1+1=2" because in the world we see that "1+1=2" and it helps us understand the world.

Why does it help us understand the world? Because "1+1=2"?

Thats just more circular reasoning.
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@Best.Korea
In the world we see geometry. True or false?
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Geometry is the science of pattern...bucky fuller

All that exists is moderation/modification of angle and frequency....B Fuller

What we have is, interfering and non-interfering patterns, operating in pure principle....B Fuller
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@Reece101
"We see" is just more circular reasoning, since you cannot prove senses without senses.
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@Best.Korea
Don’t you have any sense?

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If you and i measured our cocks , we would know " for certain "  whom has the bigger one right ?
Well.

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Ok ok.
Stop fucking hounding me.

Its  7.6 cm.
No 8 cm.
Yeah Definitely 8.

Im back.
Ive  come back after I posted this to swap the centimeters to  inches.

Then  I come back a second time and swaped it back.
Ha ha ha har

But unfortunately ill foget to do this.
Darn it.

Why You rat bastard .

▪○°•▪○⊙°•°¤▪⊙°•••▪○○°•¤《

Just invented  a game there

Post somthing real real embarrassing adout ya self  andddddd
then flirt with the unspecified  time to change it.
.
Wow.
What a fucking rush

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Only with maths can you be 100 % certain,
I mean.
Thats how Percentages work.

One can be 100% certain on any subject .   Maths will be apart of that no matter what.
Percentages.

Im 100% certain im hungry.
Thats Maths.
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Picture being 75 or  83.5% certain.

Or 13.83 % sure of something.

Whatever the fuck. " 100% certain " means.
Is "100% certain"
Buttttttt i can't be certain about that.

( Having 100% certainty brings to life "  Chance " )
Or not. ?
Im not sure what im trying to say here.

This is the winner.
♡♡♡♡♡♡♡   i will die one day. ♡♡♡♡♡♡
Thats being 100% certain
Ergo 100% certain
And 100% being the math part.

Thank you .
Thanks .
I retire.