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# infinity = -1

lightwate
I heard this somewhere, I heard it has something to do with why quantum physics is so complicated but I didn't understand how it relates. But it's interesting anyway..

If you start from number 1, add it to twice that number(Edit: 1 + 2 + 4... not 1+2+3...), then add it again to twice that number and so on... That's equal to infinity, right?

 Code: 1 + 2 + 4 + 8 + 16 + ... = infinity

You can also multiply everything by 1 and the answer is also the same...

 Code: (1) * (1 + 2 + 4 + 8 + 16 + ...) = infinity

But then 1 is equal to 2 - 1.. so we have:

 Code: (2 - 1)*(1 + 2 + 4 + 8 + 16 + ...) = infinity

Expanding/distributing, we have

 Code: 2 + 4 + 8 + 16 + 32 + ... -1 -2 -4 -8 -16 -32 -... = infinity

Everything then cancels out except for -1. so we have -1 = infinity
Afaceinthematrix
This is just wrong... For instance, where did the 6 go and where did the -3 go? You should be adding 2 times each of those numbers and then just subtracting 1 times each so then you should still get the sum of those digits which is, what we started with before multiplying by 1 which would leave it the same...
Bikerman
LOL...you beat me to it...I also can't see what the heck it has to do with QM....
Afaceinthematrix
 Bikerman wrote: LOL...you beat me to it...I also can't see what the heck it has to do with QM....

Maybe it is a red herring that's used as part of the trickery. If people see QM they think it must be very complicated and so they forget to add and/or just assume it is true without looking? Luckily, we're both skeptics and so we both spent the three seconds doing the multiplication and addition ourselves to find out that it is wrong. It's a little interesting from a psychological point-of-view (if it really is a red-herring). If people, who can normally do arithmetic quite well, see something that should be difficult, will they just overlook it and move on?
lightwate
 Afaceinthematrix wrote: This is just wrong... For instance, where did the 6 go and where did the -3 go? You should be adding 2 times each of those numbers and then just subtracting 1 times each so then you should still get the sum of those digits which is, what we started with before multiplying by 1 which would leave it the same...

woops, I typed the example wrong.. it's supposed to be 1 + 2 + 4 + 8 + 16.. the 3 is not supposed to be there. sorry. I'll edit the first post
Afaceinthematrix
So what you're essentially doing is Σ(2^(n+1) - 2^n) where n starts at 0 and goes to infinity. Some basic calculus and understanding of series will show you that this series diverges. So your thing does "equal" infinity.

You need to be careful with series that alternate between positive and negative terms because order DOES matter.
therimalaya
Infinity cann't be a number, it is meant to be something beyond the number,... I think so,... There must be something going wrong in the derivation
kelseymh
 therimalaya wrote: Infinity cann't be a number, it is meant to be something beyond the number,... I think so,... There must be something going wrong in the derivation

You should do some research on transfinite numbers.
_AVG_
I would say that this argument is flawed because of some illegal operations. Take this:

If this is one number:
2+4+8+16+.....

And this is another number:
1+2+4+8+16+.....

You can't subtract the second from the first without realizing that both of these are undefined i.e. both these series diverge. So, in fact, subtracting one from the other is an illegal operation. Addition, Subtraction, Multiplication don't work normally with infinity. And, I'm not sure, but I think that the above sums are absolutely infinite, not transfinite (I'll have to check up on this point, it could be wrong).

You cannot individually cancel out each term in a telescoping fashion precisely because there are an infinite number of terms. Consider this example to see this clearly:
1-1+1-1+1-1+......
Does this series converge or diverge?
asnani04
Good trickery. Actually the order of subtracting matters here.
2 + 4 + 8 +16 +32 +64...
-1 - 2 - 4 - 8 - 16 - 32...

This will give 1 + 2 + 4 + 8...
The series we actually started with! So this is it!
Oh, there are more confusing things that you can do with infinity if you just try and treat it as a regular number.

Infinity + infinity = ...

Yeah... you get the idea.
weed
ur wrong infinity means never ending number it maybe 10,100000 or -1,-100000
cybersa
That's interesting.
I can't able to figure it out while Expanding.

if 1+2+4+8...... = infinity means

(2-1)(1+2+4+8......)= INFINITY

(2-1)(infinity)=infinity

2infinity - infinity =infinity
hspb
Infinity is not a number.
We must define plus and multiplication correctly fo infinite sum.
Pippo90
Thanks for sharing this post! If you know something about series it's not a difficult problem, but in any case I think it's a very good example of how math can be sometimes counterintuitive.
johans
here we are again problem solving..

I just remember my college days.
gamebox
if we think, infinity doesn´t exactly exist. it´s just a maths suposition that is very useful. for understand it is necessary a lot of spacial visión.
Bikerman
Perhaps, but can you be so sure?
What about bounded infinities? Are you so certain that our universe has a 'use by' date and will one day just 'stop' ? I mean...it might, sure. I think the current favorite is heat death as the 'end state' - a sea of cold particles so diffuse that they are really hard vacuum, until the universe stretches es into essential non-existence via over-dilution.
But there is another view which is interesting.
Penrose thinks that the universe, when essentially bereft of matter, will loose track of itself. With no matter there is nothing to give scale, so what WE might consider an almost infinite expanse of cooling energy, could equally well be the protp-singularity for the next Big Bang - infinitesimally small in that reality.......
just saying.......I think a hold on the certainty might perhaps be warranted at this point, for maybe a few decillion years - just until we can firm it up a bit.....
Bikerman
More bullcraop spanned. Vortex mathematics is pseudo-scientific bull.
lemonedia
 Bikerman wrote: More bullcraop spanned. Vortex mathematics is pseudo-scientific bull.

I wouldn't go as far as to call it so, Bikerman. Finding the Digital Root of a number is legitimate mathematical practice, and is used in finding underlying patterns / behavior in fractals and seen in Programming as "Mod9()". Just because something is a new approach to a problem, with little to back up any findings, doesn't mean it's bull.

Besides, no-one knows the applications of Vortex Based Math other than it's useful for making surface-maps for toroidal structures that expose a path along the surface that correlates with Phi (loosely). The number patterning of such a surface map is also interesting to observe. Maybe i'm just more autistic than you I don't see it as a 'Science", but more a mathematical patterning tool. As a student of Linear Algebra (matrix equations), I can't dismiss interesting correlations between such configurations of numbers.

To dismiss my post for saying that "hey look, when you multiply a number by 9, and take the digital root, you end up with 9 again" in a thread about numbers that can represent infinity seems like jumping the gun based on your beliefs.

Now, I hope we can get off on a good start and have some solid discussion in these forums in the future!
Bikerman
Yes they do. There was a TED talk on it where some pratt made all sorts of claims and there are websites pushing it like the new messiah.
THERE IS NO VORTEX MATHS., There is maths, which can be used to model votices.
9/1 has nothing do do with a vortex to my eye - perhaps you can explain how a simply integer sum is related to a turbulent flow ?
Linear Algebra?. I saw this :
 Quote: think 9 is the infinity and the nothing. 9 x 1 = 9 9 x 2 = 18; 1+8 = 9 9 x 13 = 117; 1 + 1 + 7 = 9 This is a major principle behind Vortex Based Mathematics. Here's the 'nothing' part of 9: 9 + 1 = 10; 1 + 0 = 1 9 + 2 = 11; 1 + 1 = 2 9 + 13 = 22; 2 + 2 = 4 (and 1 + 3 = 4)

I still don't see any vortex and I see no infinity either,,,,
spinout
Hm, how does this work?
9*32 = 288... 2+8+8 = 18 and then again do 1 + 8 = 9 ?
spinout
Hm, another question: Base of 10? sound unnatural? Is there a map for every base to apply?
Bikerman
UNNATURALAL?
Base is just = number of distinct counters/units/symbols available. How can that be natural? iS 4 natural AND 6 not? oNLY TO A 4 FINGERED MAN i GUESS,,

Base 10 is great for arithmetic because the place value marker is easy to manipulate to give useful multiply/divides. In computing Base 10 is useless - literally - we dont tend to use it at all at low-level, where the number is 2 (binary) and the base system of choice is base 16 (hexadecimal) because it is easy to represent 8 bits in 1 hex digit. Old fashjoned computer people worked entirely in hex and most of us can't convert base 10 to Hex because we never uised base 10/
(ie we can't just go 'AF' - that is ... whatever... Obviously I CAN convert or I would be an arithmetic idiot, but we never DID convert in daily work.,..)
spinout
well, wouldn't 5 be more natural? I do not have 10 fingers on one hand...
A7 hm... 7 is 7 and A is 10 hm perhaps where this could mean 7 plus 10 times 16 hm 167 is base 10 lingo. correct?
What would be natural? Well, I have never felt good at base 10... Suppose -2 is a better base - just joking. What I mean is if there is a "vortex math" then why 10 as base? 10 base arithmetics yes - works good, but 10 base arithmetics is not vortex math! Vortex math would not be using 10 as base! hm, 60 or something is better (depends on how you divide a circle) I don't know - 10 seems out of use atleast.
spinout
Hm, a bit off topic but funny... "Marko Rodin, Master of sudoku!" I took that joke from someone else.

This is "discrete math" actually this so called vortex math. Even ordinary discrete math was abandoned sometimes in the universities I have heard in some countries. Discrete math is problably Bikermans best tool as a computer system designer or something in that area of expertice.
jajarvin
Here a funny calculation:

infinity / infinity = 1

because the number divided by itself is one.
Bikerman
But since infinity isn't a number* then the calculation is not valid.

*It is a limit.
kelseymh
 jajarvin wrote: Here a funny calculation: infinity / infinity = 1 because the number divided by itself is one.

Yes, it's funny because it's wrong. As Bikerman said, infinity is not a _value_, it is the result of taking a limit; and specifically it is the symbol for a limit which is divergent. The correct way to write the above statement is:

infinity / infinity = whatever

You have to determine the value on the right on a case by case basis. Specifically,

lim f(x)
--------- = whatever
lim g(x)

If both limits are taken for the same range of x (e.g., lim x->0, or lim x->1 or lim x->infy), then you can rewrite the ratio as the limit of the ratio of the functions:

lim f(x) f(x)
--------- = lim ----
lim g(x) g(x)

Now, you _may_ be able to simplify the argument f(x)/g(x). For example, if they are polynomials, then you could factor and resolve the ratio: let f(x) = x^2 - 2x + 1 and g(x) = x-1 (both of which diverge for lim x -> infy), then f(x)/g(x) = x+1. In that case, lim x->infy (x+1) = infy, not 1.
spinout
infinity / infinity = 1...

Ok, firstly I say jajarvin is meanin by writing the word "infinity" as a "number of something" bigger than this realtity. Bigger is not the correct word, out of this reality is the correct. So we go out of bounds really. So saying eq 1 is not false but not true either from this viewpoint.

Secondly, in a universe like this we tend to see it as a limit, as pointed out. Still the word infinity don't work at a viewpoint, so as described before "case by case" is added to see where it is heading , traditionally...

Thirdly, If you add the "case by case" viewpoint you are not seeing the meaning of the statement, and, no offence, that is wrong too. The math teachings are not so good I must say...

Finally, "whatever" is not false of course...
Bikerman
 spinout wrote: infinity / infinity = 1... Ok, firstly I say jajarvin is meanin by writing the word "infinity" as a "number of something" bigger than this realtity. Bigger is not the correct word, out of this reality is the correct. So we go out of bounds really. So saying eq 1 is not false but not true either from this viewpoint. Secondly, in a universe like this we tend to see it as a limit, as pointed out. Still the word infinity don't work at a viewpoint, so as described before "case by case" is added to see where it is heading , traditionally... Thirdly, If you add the "case by case" viewpoint you are not seeing the meaning of the statement, and, no offence, that is wrong too. The math teachings are not so good I must say... Finally, "whatever" is not false of course...

The maths being taught here was fine, until this. ∞/∞ <> 1. It might 'tend to' one, as Mike said, but you can't simply equate it to one - that is not just wrong, it is horribly confused and confusing.

Not all infinities are the same size - this is obvious, and rather important, For example, the set of integer numbers is infinite, and so is the set of real numbers, but the set of real numbers is larger than the set of integers (can easily be proved, since the set of reals can map a value to every member of the set of integers, it MUST be larger - Cantor's diagonal proof, as it is known)..There are well developed mathematical techniques and symbols for dealing with infinities, developed by Cantor and others, so we have countable infinities and uncountable transfinite infinities, The set of integers is an example of the former and the set of reals the latter (cardinality aleph null).

Equating to one is not only wrong, it is stupidly wrong, since it involves ignoring the obvious.
spinout
Cantor had an error in putting up the set of integers in the proof, as I have shown before. They do not exist in the set of real numbers.
Bikerman
Err...there us no error in the diagonal proof that I know of. Please produce your evidence.
The set of real numbers DOES include the integers - BY DEFINITION - so I haven't got a clue what you are on about here.

 Quote: The integers are the set of real numbers consisting of the natural numbers, their additive inverses and zero
spinout
Integers are for counting objects, a system of axioms. A mathematitan adding that into the realm of real numbers are not thinking correct.
Bikerman
What the hell are you taking about? I suspect you don't know.
a) Integers are NOT axioms, They follow deductively/tautologically from the peano postulates.
b) Who says they are used for 'counting objects'? Damn stupid thing to say. Number theory defines the entire series of numbers available. The reals are defined from a set of rules and the integers follow.
You are either completely out of your depth and spouting gibberish, or you are trolling.
Either way it would be a good time to stop.
spinout
The postulates are an axiom... And I am not trolling
There is another way to define integers (don't know the english word for the teaching, in Swedish it is called "amountteaching") but even then you use axioms.

I are in depth, too much and not trolling.
Bikerman
The axioms DO NOT DEFINE THE INTEGERS. They define the entire set of reals.

There are several ways to define the integers axiomatically, but the peano postulates show that they are simply members of the larger set of reals, so your earlier comments are simply nonsense.

I can draw up a set of axioms that will define all sorts of distinct number series within the entire set of reals - SO WHAT?
spinout
hehe, calm down. I shared your viewpoint before, today I have another viewpoint. Today I can't agree with your last sentence, no offence. Grouphug!
Bikerman
It isn't a viewpoint and there is nothing to 'share'. With regard to this branch of mathematics there is WRONG and there is RIGHT. There is no opinion, no viewpoint, no interpretation.
Thus the statement that the real number set (R) doesn't contain the integers (Z) is utter, utter crap and it will always BE crap. It doesn't matter whether the Pope of Maths gets every Mathematician in the Country of Maths'R'Us to agree that Z is not a subset of R - they WILL STILL BE TALKING CRAP.
It follows that Cantors diagonal proof is not vulnerable to attacks based on some misconceived and frankly, idiotic, idea that Z is not a subset of R.

It isn't so much the being wrong, it is the pretence to knowledge, followed by breathtakingly dumb nonsense that irritates me. So when you talk about proving Cantor wrong and then demonstrate that you don't understand the basic 101 stuff, then it pisses me off.
I don't mind people who don't know much about the subject - they can ask and I'll help or find someone who will. Nor do I mind people who know quite a bit, but make a couple of errors - we are all human. BUT I cannot be doing with people who pretend to know and just spout crap. The world is full of bullshit and bullshitters - wall to wall. These Science forums are a haven from the sort of bullcrap I hear and see every day, and I'll be buggered if I'm letting it into here as well.
spinout
I have no problem with frank speeking, that makes a forum.
I am not saying that Z is an idiotic idea, not a subset of R, just look at the computerworld for an instance. But when it comes to interpret the nature into Z well you wind up with having tolerances of R in voltage - and "voila!" the magic of checksums was invented.
kelseymh
 spinout wrote: I have no problem with frank speeking, that makes a forum. I am not saying that Z is an idiotic idea, not a subset of R, just look at the computerworld for an instance. But when it comes to interpret the nature into Z well you wind up with having tolerances of R in voltage - and "voila!" the magic of checksums was invented.

You continue to string words together in ways which make no sense. You also contradict yourself.
Arrogant
infinity / infinity is very WRONG
They aren't numbers. You can't just divide that.
spinout
yes, out of this reality.
While I've done these kind of calcuations in the past, if you read actual mathematical ideas about infinity, it's interesting, and hard to wrap your head around.
Afaceinthematrix
 spinout wrote: hehe, calm down. I shared your viewpoint before, today I have another viewpoint. Today I can't agree with your last sentence, no offence. Grouphug!

You're entitled to your opinion but that doesn't make it any less wrong. You can say whatever the Hell you want but in mathematics, you're required to prove it (which you cannot do because you are epicly wrong). Cantor is one of the most brilliant mathematicians of all time and to have anything less than a Ph.D. in mathematics and claim that he made a simple error (that thousands of other mathematicians with Ph.D.) is not only insanely stupid, but insanely arrogant.

The integers are a countable set and is a subset of the real numbers - which is uncountable. To prove that the real numbers are uncountable is very easy because Cantor came up with a clever "diagonal" proof. Anyways... I don't have the time or the desire to right up a set theory/number theory textbook here on an online forum.
Bikerman
Science is not a democracy and the idea is dumb. In science there are well supported theories/hypotheses and there are more speculative hypotheses - but even the latter can only be considered scientific if they are testable and make specific statements/predictions which can be put to the test (or which could, potentially, be tested one day).
If you really do have 2 Doctorates (and I'm afraid that I don't believe that, in lieu of actual evidence/support) then they are clearly in disciplines with limited scientific or mathematical content. A Doctorate in mathematics is a pretty good indicator that the person concerned understands mathematics at a level which means they probably have something worthwhile to contribute when they choose to post in a discussion. Whilst academic qualifications do not guarantee the quality (or even sanity) of the holder and their potential contributions, they provide a pretty good first-approximation in most circumstances.
spinout
I got 2 different titles from our academic schooling - and not any in math directly even if alot was that directly. But now it gets hard to precisice/reflect what I wrote since the thread must have gotten a bug and it dissapeared.

There are several schoolings in math, and that comes to play when it get down to the fundamental.
Bikerman
Ahh, that was me being too ready with the spamcan button - I think I spamcanned two postings rather than the one I intended....

Here is the text of the posting..
 spinout wrote: Which is worse; to be stupid or arrogant with an opinion? Truely, I am so stupid I can't see any way this is arrogant! So in my case beeing stupid means I can't be arrogant. So I proofed you wrong saying I can be both from my perspective Laughing Also I am Swedish, that means "democracy" i.e. there is no superior group to look up to (dictators). Rather the opposite is the natural way of looking upon things , it is a miracle we still are a kingdom. But gets quite funny when the king gets in trouble of his past living Twisted Evil In most cases the Ph.D. means nothing, I got 2, schooling is of no matter since you forget so fast what you have learned. The only thing countable in life is your attitude and E.Q mostly. The time is always the issue... Hardly got time to write anything here... I have nothing against that diagonal proof .
Sylin
This (I go back to the very first post in this thread) touches on the foundation of a branch of mathematics known as Real Analysis, you want to particularly look at sequences and series, and convergence.

Limits
 Code: 1 + 2 + 4 + 8 + 16 + ... = infinity

This expression isn't correct in the first place even you might "say" it this way in speech. Saying "The sum tends to infinity" will be more accurate.
The left-hand side is a divergent series. One can think of the series as increasing without bound, and we say that the limit doesn't exist.
I can easily consider another divergent series:
 Code: 1 + 3 + 5 + 7 + 9 + ...

and you would've written it in the same way (with the "= infinity"), which is now quite plainly incorrect because the 2 series above aren't the same (no 2 limits to compare, and one is an exponential growth while the other is a linear one).

Ordering
One can re-bracket terms in an infinite series given that it is convergent, but one can only rearrange the terms (without affecting its limit) in an infinite series if it converges absolutely.
One may be interested to know that in a special kind of series (one that conditionally converges), we can rearrange the terms to give us any limit we may choose (Riemann series theorem).
Although how you may go about computing the limits (or the lack thereof) is not within my current understanding.

But this should give you some ideas of the problems that arises when you try to expand this out:
 Code: (2 - 1)*(1 + 2 + 4 + 8 + 16 + ...)

Much rigour is needed when dealing with an infinite series. But I would guess that the original intent of this thread is to lighten up the mood with pseudo-algebra commonly found across the internet with faulty and obscure reasoning that results in absurd conclusions like 1=2 and is, by no means, a prompt for a serious mathematical discussion concerning the matter although I don't know anything about quantum mechanics and how the 2 may have an analogous connections.
Tsaycro
Though I don't know the details, the procedure of taking diverging series like these and putting a number to them (in this case -1) is called "Renormalization". It certainly has something to do with quantum mechanics, as quantum field theory is the area where this is used most often.
mshafiq
No, you just simply can't subtract infinite number of terms from each other that way. Even if you do you will be having one more infinite +ve term than negatives. So the answer still should be infinity. It looks that you can confuse simple people by just saying that, but the people with really strong mathematical background or people who have much interest in Mathematics can not be confused or deceived :p

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