Infinity * Zero = Any Number ARGUE HERE

[aperson]

Originally Posted by lord_carbo

Can you prove 1 + 1 != 2?

1 + 1 == 2 is an unprovable operation in any numerical system. It can be defined or proven from other axioms (such as Zermelo-Fraenkel Set Theory + Axiom of Choice); however, it can only be shown as a consistent statement in inconsistent systems.


But let's not go into Gödel's theories here, they would make all of your heads explode.

[Reach]

Mmm, Godel.

Indeed, an informal system such as the human mind can deduce from a formal system more than the system can actually prove or show as a whole. I suppose this is why intuitively, 1+1=2 is obvious but cannot be proven.

However, it does show that trying to explain everything as a formal system is futile, and that it is wrong to assume that proofs are truths and must be formulated on these guidelines that can never be met.

I quite like the paradoxal idea that we can see that something is true because it is unprovable.

[A2_Sauce]

Originally Posted by Reach

Mmm, Godel.

Indeed, an informal system such as the human mind can deduce from a formal system more than the system can actually prove or show as a whole. I suppose this is why intuitively, 1+1=2 is obvious but cannot be proven.

However, it does show that trying to explain everything as a formal system is futile, and that it is wrong to assume that proofs are truths and must be formulated on these guidelines that can never be met.

I quite like the paradoxal idea that we can see that something is true because it is unprovable.

you wanna try rephrasing that?

[darkdieuguerre]

Originally Posted by Reach

Mmm, Godel.

Indeed, an informal system such as the human mind can deduce from a formal system more than the system can actually prove or show as a whole. I suppose this is why intuitively, 1+1=2 is obvious but cannot be proven.

However, it does show that trying to explain everything as a formal system is futile, and that it is wrong to assume that proofs are truths and must be formulated on these guidelines that can never be met.

I quite like the paradoxal idea that we can see that something is true because it is unprovable.

Statements that can't be proven but are true are also called postulates, so 1+1=2 is a postulate. It is "obvious", yet it cannot be "proven". It's just like saying that there can only exists one line that is parallel to a given line through a point not on the given line (aka the Parallel Postulate). If the postulate is wrong, then the whole system of mathematics falls apart. If everything could be proven off of everything else, then there must be a flaw somewhere. You must make an assumption and develop off of that assumption. It's nice how dependent we are on postulates that look true but mightn't be. Just imagine if someone disproved one of those postulates...

[Reach]

Originally Posted by A2_Sauce

you wanna try rephrasing that?

Godel thinks you can find truth in something by showing it cannot be proven.

As such, that means that truth and proof are not necessarily the same things, as you would assume. Which is why it is reffered to as a paradox; you can know something is true because you can't prove it as a fact.

I'm not completely familiar with all of Godels inconsistancy theorems though, and as such probably need to read up on them....after finishing that chem assignment I've been putting off for days ;D

[A2_Sauce]

Is it true that if there is another intelligent civilization somewhere out there in the universe... they would find the exact same number as pi... but it wouldn't be 3.1415926535897932384.... because we are on a 10-number system, is this correct?

[flamingspinach]

Originally Posted by Reach

Mmm, Godel.

Indeed, an informal system such as the human mind can deduce from a formal system more than the system can actually prove or show as a whole. I suppose this is why intuitively, 1+1=2 is obvious but cannot be proven.

However, it does show that trying to explain everything as a formal system is futile, and that it is wrong to assume that proofs are truths and must be formulated on these guidelines that can never be met.

I quite like the paradoxal idea that we can see that something is true because it is unprovable.

<Reach> Mmm, Godel
<Godel> Mmm, ReachIN FOR MA FUCEN HIDDEN RIFLE/WALKING STICK
<Godel> FUCEN EVIL PROFESSORS
<Godel> I AIN'T EATIN **** FUC NO
<Godel> brb dying of starvation
<Godel> lmfao get it
<Godel> GODEL'S FIRST COMPLETENESS THEOREM
<Godel> MY WORK HERE IS COMPLETE
<Godel> QED
* Godel has quit (broken pipe)

[darkdieuguerre]

Originally Posted by A2_Sauce

Is it true that if there is another intelligent civilization somewhere out there in the universe... they would find the exact same number as pi... but it wouldn't be 3.1415926535897932384.... because we are on a 10-number system, is this correct?

It depends on the base that the other civilization uses. If they use base 10, we should have the same number. Otherwise, the number should be the same, just represented in whatever base they have, but converted to base 10 the number should be correct.

[foolishwun]

wait wait

Inf - Inf = undef?


inf - inf = 0
cus for the exact same value over 0 the positive inf is it is completely undone back to 0 by the negative inf in the exact way it is increased from 0

[RandomPscho]

Infinity isn't a value though. It is something that is unbounded and has no numerical value.

[foolishwun]

exactly.
and whatever is is minus whatever it is makes it come all the way back to zero no matter what it means

[businessman07]

thread is still going strong, math is like proving nothing is somthing. we breath air, but what is air? atoms stuck together?

[foolishwun]

whats with the people saying 1 + 1 dosnt equal 2
its not "relative"
1 always = 1
if you have 1 apple and i give you another apple, you will have 2 apples
didnt we learn this in grade 1

[businessman07]

how do you know 1 = 1?

[darkdieuguerre]

Okay, Infinity - infinity != 0. (!= means not equal to).

Since infinity is not a value, we must use calculus. Take the examples:

lim (x->inf) e^x-x = infinity.

lim(x->inf) x-e^x = -infinity.

1=1 by the Reflexive Property. However, 1+1=2 cannot be "proven". If you read a few more posts, maybe you'd realize that the discussion revolved out of some spam.

[TheRapingDragon]

Not going to even attempt to get into this whole debate, far too above me for math, but wanted to address one point.

Originally Posted by foolishwun

1 always = 1
if you have 1 apple and i give you another apple, you will have 2 apples
didnt we learn this in grade 1

Is every single apple the same weight, the same density, the same amount of juice, is every single apple in this world identical. No. If the answer was yes then 1 = 1, but looking at apples (or any other item) you could easily say that apple 1 is 0.999812% different from apple 2, thus 1 would = less than one. So 1 /= 1.

In that way it is possible to define that 1 does not always equal 1, and so this debate is possible.

You can even bring this theory up to 1 + 1 = 2.

If apple one is 99.112% of apple two, then you are really doing 1 + 0.99112 which doesn't equal 2. So many possibilities.

[fastfingers65]

..........

[darkdieuguerre]

Originally Posted by TheRapingDragon

Not going to even attempt to get into this whole debate, far too above me for math, but wanted to address one point.



Is every single apple the same weight, the same density, the same amount of juice, is every single apple in this world identical. No. If the answer was yes then 1 = 1, but looking at apples (or any other item) you could easily say that apple 1 is 0.999812% different from apple 2, thus 1 would = less than one. So 1 /= 1.

In that way it is possible to define that 1 does not always equal 1, and so this debate is possible.

You can even bring this theory up to 1 + 1 = 2.

If apple one is 99.112% of apple two, then you are really doing 1 + 0.99112 which doesn't equal 2. So many possibilities.

Now that's just irrelevant. An apple cannot be a percentage of something else because it is an object that exists in a certain state. If an apple is larger or smaller than another apple, that makes it an apple, and just an apple. An apple is an apple regardless of the size, type, etc. You can say that you have 98% of an apple by cutting 98% of an apple, but you can't say that a whole apple is 98% of another apple without using size, or some other quality.

1+1=2 is a postulate. It cannot be proven, so it is assumed to be true so our whole system of mathematics works.

[lord_carbo]

Originally Posted by darkdieuguerre

1+1=2 is a postulate. It cannot be proven, so it is assumed to be true so our whole system of mathematics works.

It's not assumed to be true, it is.

Originally Posted by 3D OGRE 1

do you even know what you are talking about?

Do you? All you said in response to my post was "do you even know what you are talking about?" as if you do... yet you never correct anything that I said! Man, that's stupid.

To save your time, I'll answer for you: You don't. Merely because you think 1 + 1 can equal anything other than 2.

Originally Posted by TheRapingDragon

Not going to even attempt to get into this whole debate, far too above me for math, but wanted to address one point.



Is every single apple the same weight, the same density, the same amount of juice, is every single apple in this world identical. No. If the answer was yes then 1 = 1, but looking at apples (or any other item) you could easily say that apple 1 is 0.999812% different from apple 2, thus 1 would = less than one. So 1 /= 1.

In that way it is possible to define that 1 does not always equal 1, and so this debate is possible.

You can even bring this theory up to 1 + 1 = 2.

If apple one is 99.112% of apple two, then you are really doing 1 + 0.99112 which doesn't equal 2. So many possibilities.

One apple represents the quantity of one. Stop being overly technical by saying all apples are different. Well, okay, they're all different, but an apple is still an apple, regardless of mass, size, etc.

[Reach]

Originally Posted by flamingspinach

<Reach> Mmm, Godel
<Godel> Mmm, ReachIN FOR MA FUCEN HIDDEN RIFLE/WALKING STICK
<Godel> FUCEN EVIL PROFESSORS
<Godel> I AIN'T EATIN **** FUC NO
<Godel> brb dying of starvation
<Godel> lmfao get it
<Godel> GODEL'S FIRST COMPLETENESS THEOREM
<Godel> MY WORK HERE IS COMPLETE
<Godel> QED
* Godel has quit (broken pipe)

...XD

1+1=2 is a postulate. It cannot be proven, so it is assumed to be true so our whole system of mathematics works.

Using Godel numbering you do not really need to assume anything. I am well aware of the use of axioms and such as the foundation for...well, everything, but that is not really what I was talking about.