160 replies to this topic

[sabriath]

I have absolutely no idea what that means, but I love it.

What I meant by scalable is that in a world where "0.9999999999999999999999999999~" is the highest number known, then "1" is infinite to them. Any number that you can imagine as being the biggest number possible, infinite is JUST beyond that reach. In infinite axioms, all proofs are based on concepts of the mind (since infinite is unreachable). If I remember correctly they are:

inf + @n = inf
inf - inf = @n
inf - @i = inf (where @i = @n but not inf)
inf * @n = inf
inf / @n = inf
etc.

Because of the asymmetry of the axioms themselves, it makes it almost pointless to make proofs using it. My feelings of infinite should ONLY be used in iterative sequences (like limits), not used as actual numbers that can be substituted. But that's just how I feel, and like that matters in that world.

Do you disagree both sets have the same number of elements? And that there's a one-to-one correspondence between the two sets? Or do you think one set is larger than the other?

If you have a set of all numbers, and a set of all odd numbers out of that set, then yes...you would have exactly half the numbers in the subset as the full set, even when expanded to infinite. If I were to be the one to create infinite axioms, it would be symmetric as:

inf + @n = @n + inf
inf + inf = 2 * inf
inf - inf = 0
inf - @i = -@i + inf
inf * @n = @n * inf
inf / @n = inf / @n
etc.

Using infinite as an unknown variable instead of a concept, then it works in all contexts of the rational math world. It would be the same as if you used "x" to substitute infinite since infinite is unknown anyway (and all math identities still apply properly). No special cases required *shrugs*.

But like I said, it's just how I feel...and it's not like my ideas would ever change anything.

[blue_chu_jelly]

What I mean by that is, "infinite + infinite = infinite" right? So with that we can say that "1 + 1 = 1" because any number can substitute for infinite as long as that number is larger than any number known (although 1 is not, it is scalable).

But I remember reading that infinity is not a number, rather a concept and it isn't part of the set of real numbers. So you can't just choose any number to replace it with and say "54788 + 54788 = 54788".

[KC LC]

Do you disagree both sets have the same number of elements? And that there's a one-to-one correspondence between the two sets? Or do you think one set is larger than the other?

If you have a set of all numbers, and a set of all odd numbers out of that set, then yes...you would have exactly half the numbers in the subset as the full set, even when expanded to infinite.

I was afraid of that. You've gone horribly wrong here. Nothing much about Banach-Tarski matters if you're this confused about cardinality.

inf + inf = 2 * inf

You know, posting that could get you into trouble on a real math forum. But seriously, how can anybody make sense of "2 * infinity"? What could that possibly mean?

[~Dannyboy~]

inf + inf = 2 * inf

You know, posting that could get you into trouble on a real math forum. But seriously, how can anybody make sense of "2 * infinity"? What could that possibly mean?

There are a whole magnitude of issues with treating infinity as a real number. The way I see it, as infinity approaches membership into the set of real numbers, all other real numbers approach zero. They all become indiscriminate and infinitesimal in comparison.

[sylvan]

I was afraid of that. You've gone horribly wrong here. Nothing much about Banach-Tarski matters if you're this confused about cardinality.

^ this.

If you treat infinity as a simple variable, you should be able to prove most anything:
1/infinity = 0 (because your dividing a finite amount into infinite pieces)
therefore 1 = 0*infinity (basic property of multiplication and division being the reverse of each other)
therefore 1=0 (since 0*anything = 0)

Now with the proof 1=0, I can now show 1+1=0 or 0+0=1 or even 1+0=2. woo.

[C-c-JEC-c-C]

I'm a bit confused lately.
I don't know if this is the right place but... what's the answer to: infinity + math/1?

I've been told by most mathematicians that they don't understand what I'm talking about and that what I'm saying makes no sense.

So I guess if you add math, you're adding everything of the known mathematical system to infinity, and infinity is the unknown... So it's like:

x + infinite knowledge/1, isn't it?

I came up with a new concept: Whole Exknowledge.

Now we can acknowledge and exknowledge things!

I also found a cool website!
http://www.blackplanet.com/exknowledge/

Edited by C-c-JEC-c-C, 15 July 2010 - 03:53 PM.

[Erik Leppen]

any number can substitute for infinite as long as that number is larger than any number known

There is no number that is larger than any number known. This makes your statement a vacuous truth

Besides, infinity is not a number. It's a concept.

inf + inf = 2 * inf

You know, posting that could get you into trouble on a real math forum.

Why? It's a true statement. We have inf + inf = inf and we have 2 * inf = inf. Both sides equal infinity, so they equal each other. So inf + inf = 2 * inf. What this doesn't imply however, is that inf + inf != 3 * inf.

But seriously, how can anybody make sense of "2 * infinity"? What could that possibly mean?

2 * infinity is just infinity, just like infinity + 1 is infinity. Nothing special about that

[C-c-JEC-c-C]

Besides, infinity is not a number. It's a concept.

Is "number" a concept?
So what's 5/number+1?

So, I think that's one of the reasons he thinks "infinity" can be a variable. Although, if that's one of the reasons he thinks that, I will disagree with that as I think (ah I don't know much about this subject, but here goes) infinity can't take the place of a number because numbers aren't infinite. Is that right? lol I hope so.

Edited by C-c-JEC-c-C, 15 July 2010 - 04:08 PM.

[makerofthegames]

What if I take a negative number infinitely small, and a positive number infinitely large, and add them together?

[sabriath]

I stated in my post that infinite right now is a concept....and you argue against me saying it's a concept? Which is it then...a concept or a concept?

Anyway, the point I was making is that how *I* feel is that infinite shouldn't be a concept but a substitute for a number we just cannot reach, which would prove B-T wrong. It would also bring infinite into the rational space of mathematics...no current rational proofs need to change or be opted out for it. As I also stated, my opinion doesn't matter.

I was afraid of that. You've gone horribly wrong here. Nothing much about Banach-Tarski matters if you're this confused about cardinality.

I can't be horribly wrong if it was my opinion on how things 'should be', and it's not like math theorists of infinite space can prove what *I* say wrong, nor can I prove what they say wrong because infinite is an invisible range. Maybe the concept they they have derived is valid within their context...and defined by it, so maybe I should rename mine something completely different and mean what I conceptualize? I'll call it biff then lol

I'm not confused about cardinality either...it's simple, in THEIR realm of concepts, a set of all numbers is 'infinite', and a set of all odd numbers is 'infinite'....and since 'infinite = infinite' they must be the same right? But that's crap logic and you know it, any 4 year old can reason that you have exactly half of the other set no matter how long you count for, so these sets are not equal....it wouldn't happen with a biff unit.

therefore 1 = 0*infinity

This would be false even in the normal proofs:

1/x = 0, if this is true then we can also have
1/0 = x, which is false because 1/0 is dne

What would be better stated would be:

1/inf = ~0, therefore
1 = inf * ~0

That's as far as you can go since ~0 is a limit, not an actual solid unit. Just the same you have:

1/~0 = inf
1/0 = dne

But note that these are all if 'inf' were in the rational realm....these formulas are not how they currently work (entirely), which is a pitty since they work so well. Too bad I cannot introduce biff into the community *sigh*


edit:

What if I take a negative number infinitely small, and a positive number infinitely large, and add them together?

In normal concepts, it would still be infinite I think. In biff it would be:

inf + ~0 = ~inf

where ~inf can be treated as inf, but cannot be used in congruence with it.

Edited by sabriath, 15 July 2010 - 07:26 PM.

[KC LC]

I can't be horribly wrong if it was my opinion on how things 'should be', and it's not like math theorists of infinite space can prove what *I* say wrong...

sabriath, you can't change fundamental principles of mathematics just to suit your particular views. Even the smallest change would cause a tsunami effect throughout mathematics -- much more far-reaching than just the issues discussed in this topic.

I'm not confused about cardinality either...it's simple, in THEIR realm of concepts, a set of all numbers is 'infinite', and a set of all odd numbers is 'infinite'....and since 'infinite = infinite' they must be the same right?

No, it's not that simple. All infinite sets do NOT have the same cardinality. For example, the cardinality of the continuum (the real numbers) is larger than the cardinality of the integers -- yet both sets are infinite.

I can't believe we're even having this discussion. These facts aren't open to debate, or subject to someone's opinion. They're part of the very foundations of mathematics.

You might as well just declare that pi = 3. That makes about as much sense.

[sylvan]

1/x = 0, if this is true then we can also have
1/0 = x, which is false because 1/0 is dne

You can't have 1/x = 0 in regular mathematics, because x is a finite number. Any number divided by a finite number must be a finite number itself. Therefore, division by zero is undefined, because it requires an infinite number of divisions. However, if you allowed x=infinity, then you can have divisions by zero.

1/inf = ~0, therefore
1 = inf * ~0

Then you've just invented an impossible number. ~0 is now an infinitely small number, that when multiplied by anything aside from infinity, equates to itself, and when multiplied by infinity, equates to 1.

According to your new number
1/inf =~0
100/inf = ~0

~0*inf = 1
~0*inf = 100

1=100

Eevn using your logic. You still can prove anything at all.

[Kyle_Solo]

What if I take a negative number infinitely small, and a positive number infinitely large, and add them together?

In normal concepts, it would still be infinite I think. In biff it would be:
inf + ~0 = ~inf
where ~inf can be treated as inf, but cannot be used in congruence with it.

I think makerofthegames meant:

[Tepi]

What would be better stated would be:

1/inf = ~0, therefore
1 = inf * ~0

That's as far as you can go since ~0 is a limit, not an actual solid unit. Just the same you have:

1/~0 = inf
1/0 = dne

But note that these are all if 'inf' were in the rational realm....these formulas are not how they currently work (entirely), which is a pitty since they work so well. Too bad I cannot introduce biff into the community *sigh*

You are ignoring important data - the correlation between that ~0 and that inf of yours:


This is, I believe, what you meant, but in a form where it actually works.

division by zero is undefined, because

Division by zero is undefined because:

I can't be horribly wrong if it was my opinion on how things 'should be', and it's not like math theorists of infinite space can prove what *I* say wrong...

sabriath, you can't change fundamental principles of mathematics just to suit your particular views. Even the smallest change would cause a tsunami effect throughout mathematics -- much more far-reaching than just the issues discussed in this topic.

Even worse, everything just became meaningless and he's deriving anything.


 

For anyone with something to say about infinities and infinitesimals, read this topic. Most of your nonsense is answered there.

[sabriath]

sabriath, you can't change fundamental principles of mathematics just to suit your particular views. Even the smallest change would cause a tsunami effect throughout mathematics -- much more far-reaching than just the issues discussed in this topic.

Yes I can...I can do whatever I want, just like creationists can claim to believe in the existence of an invisible creature...I can create axioms of laws in mathematics where those axioms apply new meanings. Whether or not my ideas about it matter to anyone but myself is not on debate here...but rather the fact that I am allowed to do it because I cannot be proved wrong for it. Showing that I can do whatever I want as long as proof cannot be made against, wouldn't that be the whole point that shows 'intuitionism' is wrong...or at least wimsical rambling? This brought up the whole excluding the middle thing, and since I cannot prove nor disprove FOR my ideas, it is just considered 'unproven' rather than false....same with current math on infinite.

I know that there are a LOT of things that have been "proven" using these axioms of math, but the proofs have not crossed the threshold of rational numbers. These things are still all in thought, and where is the practicality in it? Where are the real-world solid pieces to prove it. The Bose-Einstein condensate using Riemann zeta at 3/2, or the Stefan–Boltzmann at zeta 4? Countless others found by using infinite in a limit situation...not as an actual variable. Because as Tepi mentions and others....INFINITE IS NOT A NUMBER. I know this and I'm not stating otherwise, but B-T is by substitution factors (and it seems no one sees it but me). It was the whole point of my rambling about how *I* feel of math, and how *I* classify it.

No, it's not that simple. All infinite sets do NOT have the same cardinality.

Then why were you saying that I didn't have a clue about cardinality? I stated that one was half as big as the other, and you said "you don't know cardinality". Then I stated about both sets being infinite, and you say now "they aren't the same"....if they aren't the same, then my first assertion was right, if they are the same, then my second one was right? Now I'm just getting confused, both can't be wrong. I even looked it up before I said anything the second time.

You can't have 1/x = 0 in regular mathematics, because x is a finite number. Any number divided by a finite number must be a finite number itself. Therefore, division by zero is undefined, because it requires an infinite number of divisions. However, if you allowed x=infinity, then you can have divisions by zero.

Not in my work...you can't divide by 0 even with infinite. The only time you can is with 0/0 which yields @n.

According to your new number
1/inf =~0
100/inf = ~0

~0*inf = 1
~0*inf = 100

1=100

Not in my math constructs, ~0 does not equal ~0 in my classification, they are separate entities altogether if they were derived in separate statements. In fact, the error is moving 'inf' to the other side, I got carried away, you cannot do that. The reason is because the expressions I showed were shorthand for:

lim(1/x, x->inf) = ~0

And to multiply by inf would not move the '1' to the other side, you'd just have:

lim(y * lim(1/x, x->inf), y->inf) = lim(~0 * x, x->inf)

But I got carried away, like always.

I think makerofthegames meant: {inf-inf}

Well he said "infinitely small" which is lim(1/x,x->inf) which to me is ~0. And yes Tepi, I am using "~" symbol in an approximation of the answers to a limit function. I don't know how to get those neat math symbols pretty-printed for me, so I do it shorthand.


I think we are getting carried away into placing intuitionism and higher math concepts into the realm of religion. Instead of biting my head off at every wrong thing that I have written because it "does not conform to current math" and your belief in it is so high...why don't you prove me wrong using normal math foundations? Prove to me that the following constructs are wrong:

1/inf = ~0 {which is lim(1/x, x->inf) = asymptote to 0}
inf + @n = @n + inf {which is lim(c + x, x->inf)}
inf - inf = 0 {which is lim(x - x, x->inf)}
inf - @i = -@i + inf {which is lim(x-i, x->inf)}
inf * @n = @n * inf {lim(x*c, x->inf)}
inf / @n = inf / @n {lim(x/c, x->inf)}

0/0 = @n (because 0*@n = 0)
@n/0 = dne (Tepi explained this one, apart the obvious that 0*@ = 0, @ must be 0, and if it's not, then the statement is false regardless)

In all the situations, "x" is a substitute variable for an infinite limit....which to me means that you are just replacing the variable with infinite and looking at the solution (but in a more brute-force manner because there's not enough time or space in the universe to calculate such a direct function), which suggests that infinite IS a number, but we just can't reach it ...ever. If we think of it like a number, then we can just use it as a variable, and all those conceptual millennium puzzle prizes become quite easy to understand (and even solve).

Next I show you how to win the Riemann puzzle prize!

[Yourself]

I can create axioms of laws in mathematics where those axioms apply new meanings.

You can't just create any set of axioms, they must be consistent. If they're not consistent they're completely useless. If they're consistent they may range in usefulness from mostly useless to useful.

Showing that I can do whatever I want as long as proof cannot be made against, wouldn't that be the whole point that shows 'intuitionism' is wrong

No.

the proofs have not crossed the threshold of rational numbers

What is this supposed to mean?

but B-T is by substitution factors (and it seems no one sees it but me)

I wonder why that is. I also wonder what "by substitution factors" even means.

and you say now "they aren't the same"....if they aren't the same, then my first assertion was right

No, that's not what she said. She said that not all infinite sets have the same cardinality. This is not the same as "all infinite sets have different cardinality". It also does not mean that two infinite sets can't have the same cardinality. They can, but you can't say that they do based purely on the fact that they're infinite.

Then why were you saying that I didn't have a clue about cardinality?

Because you don't. The set of odd integers has the same cardinality as the set of integers. The rational numbers have the same cardinality as the natural numbers. The cardinality of the real numbers is larger than the cardinality of the natural numbers. The cardinality of the interval [0, 1) is the same as the cardinality of the real numbers. The cardinality of the complex numbers is the same as the cardinality of the reals. Two sets have the same cardinality if we can put them into a bijection. This definition is used because it works on both finite and infinite sets. By this definition, the set of odd integers has the same "size" as the set of integers even though the set of all integers contains entirely the set of odd integers in addition to elements that are not in the set of odd integers (the even integers).

Not in my work...you can't divide by 0 even with infinite. The only time you can is with 0/0 which yields

You leave division by zero undefined but not 0/0? That's probably inconsistent and likely useless.

~0 does not equal ~0 in my classification

Why? What purpose does that serve?

why don't you prove me wrong using normal math foundations?

Because you're defining things outside of the realm of mathematics. At best we can show that your system is inconsistent. But we can't even do that unless you give us some actual definitions. As it stands there's no way to understand what you're actually trying to do.

1/inf = ~0 {which is lim(1/x, x->inf) = asymptote to 0}

What is ?

?

?

Is true for any positive real number a?

inf + @n = @n + inf

Okay, whatever the hell @n is, addition of it with infinity is commutative. You need to define addition of these two elements before you can declare it's commutative. Commutativity usually must be proven to be a property from the definition. You can't declare by fiat that it must be commutative. What the hell is n?

inf - inf = 0 {which is lim(x - x, x->inf)}

How is it not also ? Or, more generally, given two functions:



How can we say that ?

inf / @n = inf / @n

Can't complain that something is equal to itself. I can point out how silly it is to mention it, though.

Of course none of this is a proof because you didn't give enough to prove it wrong. You've intentionally left these things so vague that if I were to show anything wrong with them, you have enough wiggle room to just come in and say "oh, well that's not how it really works". Here, prove this wrong:

all those conceptual millennium puzzle prizes become quite easy to understand (and even solve).

Dunning-Kruger. Also, I'd hardly characterize the Navier-Stokes problem a conceptual one. That has very physically real implications.

[~Dannyboy~]

What the hell is n?

I think he's using @n as a (real?) constant. My calculator uses @0, @1, @2, @3, etc. for constants.

Edited by ~Dannyboy~, 16 July 2010 - 05:13 AM.

[KC LC]

sabriath, you can't change fundamental principles of mathematics just to suit your particular views.

Whether or not my ideas about it matter to anyone but myself is not on debate here...but rather the fact that I am allowed to do it because I cannot be proved wrong for it.

Yes they ARE on debate. This isn't a religion forum -- it's a math forum. Your ideas have been proven wrong several times, by showing that they lead to contradictions.

I think we are getting carried away into placing intuitionism and higher math concepts into the realm of religion.

I agree, and YOU are the one who's doing it. You make unjustified claims and then challenge others to disprove them. When they succeed, you claim it's just their opinion. Religion may work that way -- but mathematics does not.

I don't want to forbid anyone from participating in this discussion, so you're free to post here. But please take a moment to read those posts explaining why your "ideas" are incorrect -- instead of just repeating the same claims.

[C-c-JEC-c-C]

Most of what Sabriath said is way over my head.. and all that other stuff too.
But I don't think this place is a playground and I'm unfamiliar with these rules so it's hard to know if what I'm saying really means anything. But I think the thing about maths is that when a person isn't a complete expert on the subject, he can come up with ideas that are probably even way over his own head. It's like being a mystic and it feels good! It's such a dream...

Edited by C-c-JEC-c-C, 16 July 2010 - 12:36 PM.

[sabriath]

What is this supposed to mean?

Was it that hard to understand? I thought it was very clear:

Rational numbers are those that everything in this universe can comprehend pretty easily. Things like how many electrons are in orbit around a nucleus of an atom, or how much money is in my pocket...or how many bananas does the ape have. Irrational numbers are things like square root of negative numbers, or concepts about infinite. I thought this was a pretty easy understanding, but whatever.

No.

Yes? You didn't prove my statements wrong, and they apply in rational space, so I'm closer to the truth than the mathematicians we have. Oh wait, maybe you won't understand this, so let me draw it for you:

I wonder why that is. I also wonder what "by substitution factors" even means.

Because B-T is based on splitting a ball into "infinite" pieces and by translating you get 2 equal balls of the same volume. This very thought pattern is based on "infinite" being an equality variable when it isn't because as everyone clearly stated INFINITE IS NOT A NUMBER. This is how B-T approached the problem:

X/infinite = 0 (a ball split into infinite pieces)
2*X/infinite = 0 (2 balls split into infinite pieces)
0=0 (equality)
X/infinite = 2*X/infinite (substitution)
X = 2*X (reduction)

As you can clearly see, this is completely irrational thinking, and you have to be an idiot to believe it as true. The main problem with it is that you can NEVER reach infinite, so you cannot disprove it either, and what do we call things we cannot falsify?

Why? What purpose does that serve?

Simple, in the above experiment with B-T, you would get the following using my axioms:

X/inf = ~0
2*X/inf = ~0
~0 != ~0
X/inf != 2*X/inf

Pretty simple to understand, however the "!=" is not an exact "does not equal" but more of a "is improbable of being equal". Because obviously no matter how many times you divide a ball up (even infinitely), you will never be able to make 2 of them using the same pieces.

Because you're defining things outside of the realm of mathematics. At best we can show that your system is inconsistent. But we can't even do that unless you give us some actual definitions. As it stands there's no way to understand what you're actually trying to do.

No I'm not, I've created new arrangements and symbols for math that DO apply to rational concepts using some irrational regions. They are consistent in math because math has "lim" function, and I'm using "lim" function...so what's the problem? Can you not prove those that I wrote wrong? Anyway, here are your answers:

-1/inf = -~0 {lim(-1/x, x->inf)}
+a/inf = ~0 {lim(a/x, x->inf) as long as 'a' is not 0}
(~0₁ + 0)/2 = ~0₂
+a >= ~0 >= 0

Okay, whatever the hell @n is, addition of it with infinity is commutative. You need to define addition of these two elements before you can declare it's commutative. Commutativity usually must be proven to be a property from the definition. You can't declare by fiat that it must be commutative. What the hell is n?

@n is "any number" (rational). I was showing that you cannot reduce "inf+@n" to simply "inf" just by the concepts that "inf" is too large and engulfs all of the variables....adding something simply is commutative to it, it doesn't get reduced (numbers in my world do not just disappear).


lim(x² - x, x->inf) would be: inf*inf-inf...not the same as inf-inf. Again, numbers do not disappear in my world, "infinite" is an unknown and unreachable state, but if the answer is ever figured out it can easily be substituted without rewriting everything. To me it's just another variable with special properties (just like 0 has special properties).

How does f(x) not equal g(x) if they contain the same equations? You can't start with a false and try and disprove my system by coming up with a false with it. That's like me starting with "a=b" knowing that "a=1" and "b=2".

If you have: f(x)=inf, g(x)=inf
Then it must be that: f(x)=g(x)

However, I think you meant to say that: f(x)=lim(x², x->inf), g(x)=lim(x, x->inf)
Therefore you are right to conclude that: f(x)!=g(x)
But it works in my system as well:

f(x)=inf*inf
g(x)=inf
f(x)-g(x) = inf*inf - inf != 0

Of course none of this is a proof because you didn't give enough to prove it wrong. You've intentionally left these things so vague that if I were to show anything wrong with them, you have enough wiggle room to just come in and say "oh, well that's not how it really works".

That's how irrational mathematics works isn't it? As long as you start with some basic and invisible axioms, you can arrive at some off-the-wall crap can't you (like B-T)? I mean, currently you have, in mathematics today:

inf + @n = inf

That's absorption...any number you feed it is gone....and by that axiom alone, you can create some wondrous and crackpot stuff. At least you can use rational math in disproving MY axioms, if you'd like to try.

Yes they ARE on debate. This isn't a religion forum -- it's a math forum. Your ideas have been proven wrong several times, by showing that they lead to contradictions.

None of my stuff has been "proven" wrong...if you are referring to the whole spinning space station gravity thing (where has one been built to prove me wrong?), or do you mean all of these axioms (because I don't see a proof yet given to disprove it). I'm actually not producing something off-the-wall...I'm only extending rational mathematics into the irrational region, that's all. All of the axioms used in normal math such as:

a+b=b+a
a+0=a
a/1=a
etc.

Where "a" and "b" are rational numbers can be easily substituted for "infinite" and given those same properties and treated as-if it were a real number, but it's not, so I gave it a few _extra_ properties such as the ones I listed with "~" used. I don't see why we cannot challenge the math community a little bit and possibly come up with something original...what's wrong with that? A KCLC-Yourself-Sabriath hypothesis or something lol.

I mean intuitionism itself is about conceptualizing math in this same way isn't it? And wouldn't it stay on topic if we start spouting our own conceptualizations and proving/disproving them? What do we have to lose but a little time we were going to waste spouting in anger at each other anyway?