Are there any Flaws in Math?

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If we worry about 0.99999...
Why don't we worry about 1.00000... ?

If something strange is going to happen to one it is just as likely something strange to happen to the other.
Both are followed by an infinite number of digits.
Both have the same possibility of being different than they appear.
We have become comfortable with 1(.0000) but 0.9999... is foreign and makes us uncomfortable. Maybe the fact is we should not be so complacent about 1.00...

We are neurotic, but not about the 0.9999....
we are neurotic about being so at ease with 1.0000...

Part of the problem with 0.99999... is we treat it as a calculation 9/10 + 9/100 + . . . a sequential process.
That magnitude of stuff exists in this very instant without end.

Maybe it is better to think of 0.99999... and 1.0000... as different representations of the same number.

I feel like i am arguing against something,
*slaps self*
But it is excellent that people have problems with this,
it means your mind is engaged.

Maybe it is because it is sort of radial.
There is more of the weight of 0.999... expressed peripherally whereas the 1.0 is more compactly represented. The whole/most of its mass/magnitude is collected into a single digit. 0.9999.... in a sense is the same number with its representation spread out over an infinite number of places. Cantilevered and cantilevered and cantilevered and so on. In our imagination that topples easily. If you limit the precision/digits right of the point then 1 remains intact but 0.999... loses some good portion of itself.

we have 1, we set 1/10th of it aside and represent the remaining 9/10ths.
of that 1/10th we set 1/10th of that (1/100th) aside and represent the remaining 9/10ths (9/100ths) and so on and so on.

think of 0.9999... as 1 on the run caught on film in a blur. As opposed to the still-life shot of one at rest.
or 0.9999... is one seen from a different angle with perspective.
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Not to throw this thread right away, but this discussion has been taking place already in this thread... Quite thoroughly I think...

The equation of a circle.
Y = Mx + C
But what is saying that the formula shouldnt really be
Y + b = Mx + c - q
But since the values B and Q are so munute, or cancle they are not included.

That is actually the equation of a straight line.
Also, since b, c, -q are contants they can just be replaced by one symbol without loss of generality.

The only flaws in maths are when a system has not been developed correctly and paradoxes are produced. An exapmle such as Torricelli's Trumpet was only a paradox because calculus had not been invented, similarly for Zeno's paradox. Russell's paradox is another example of a paradox pointing out a flaw in the basic mechanics of a mathematical system. Russell went back to the drawing board with set theory and built his own methods (theory of types) which rule out the famous paradox (at least i was told it does).

So basically I'm saying the only flaws in mathematics are human ones.

Originally posted by cmdrpaddy
So basically I'm saying the only flaws in mathematics are human ones.

I agree with this statement cause i have been researching and I am not finding actual "errors" with math. I see that things like Xeno's paradox and such are results of a lack of mathmatical knowledge. I just posted this to see if I had missed anything. I'm sorry to sound ignorant but I am in High School so I am currently in Algebra so when you speak of Calculus I am thrown off crazy stuff from what I have seen. So my mathmatical is also very limited because the equations that I have been exposed to have been to merely make both sides = (equal) or to solve for x which is the same thing. So even those cricle equations were throwing me off Kinda sad really.

Originally posted by SpookyVince
Not to throw this thread right away, but this discussion has been taking place already in this thread... Quite thoroughly I think...

But this thread is the square root of that imaginary thread, logarithmically speaking.

This thread needed all six cybercoordinates to reach it. The imaginary/complex one required only five of them, paradoxical indeed. Proof of this lies in the fact that you cannot open both threads in the same window, without using the irattional cyber-e.




rattus norvegicus is an irrational rodEnt.

[edit on 17-4-2005 by MaskedAvatar]

Originally posted by MaskedAvatar

Originally posted by SpookyVince
Not to throw this thread right away, but this discussion has been taking place already in this thread... Quite thoroughly I think...

But this thread is the square root of that imaginary thread, logarithmically speaking.

This thread needed all six cybercoordinates to reach it. The imaginary/complex one required only five of them, paradoxical indeed. Proof of this lies in the fact that you cannot open both threads in the same window, without using the irattional cyber-e.




rattus norvegicus is an irrational rodEnt.


English please:

: wow that went right over my head
[edit on 17-4-2005 by MaskedAvatar]

The following is from memory, so please consider this if someone looks into it more deeply and finds that I made a mistake.

The intensity of a light source is derived as the square of the wave equation that defines it. For example, Psi = e^i*phi. This can be re-written as Psi = cos(phi) + i*sin(phi). Part of the equation is real, the other imaginary. Intensity is proportional to Psi^2. The result of squaring the wavefunction will be different if one ignores the imaginary part. Comparing reality to theory finds that imaginary numbers are necessary.

Strange but true. Imaginary numbers are ubiquitous in quantum electronics.

Interestingly, and annoyingly (at least to me), many engineering texts use 'j' to indicate the imaginary number instead of 'i'.

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isn't i used in calculating electric fields as well?

Reality is imaginary?
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Whatever genius decided to call products of the square root of minus 1 imaginary numbers has no idea of the trouble he has caused. He has left countless numbers of students with the impression that there is something weird and magical about that silly little number. i is called imaginary purely because at the time it seemed to be completely insane, without any logical use, hence imaginary. However there is nothing really imaginary about it, no more than root 2 is imaginary because you cannot position it exactly on a number line. i is just another number, it may have some strange properties but it is just another number.

also j is used in engineering text books because i is the symbol for current.

I know of at least one flaw, or what I thought was a flaw until a rather intelligent friend of mine tried to prove me wrong. Why do we start all our counting with 1 and then after reaching 9 we finally decide to throw in the 0? I thought it would be better if we started off at zero so that we can group all single digits together in ten. 0,1,2,3,4,5,6,7,8,9 then 10,11,12,13,14,15,16,17,18,19. I always felt the single digits were being snubbed out of the joy of having a zero amungst them while everyone else has one. Besides the point, zero needs to be used more often, not as the value but as the starting point. Everything starts from zero (zero point), so why not include our numbering system?

[edit on 18-4-2005 by Frosty]

Originally posted by FrostyWhy do we start all our counting with 1 and then after reaching 9 we finally decide to throw in the 0?

It's actually used more often than you think. In the computer science field (Which I work in) 0 is understood to be the first number. Still it does seem a bit awkward. Every time you count n items you have to end with n-1 as the last item in the list. The whole decimal system is really odd. We only use it because we have 10 fingers to count with. binary is much more simple.

Originally posted by The_Final
English please:

: wow that went right over my head

In truth I think it got under your radar. All my "math" was flawed.

But I don't think that you can prove that 2 = 1. Because it isn't.

Originally posted by Frosty
Everything starts from zero (zero point), so why not include our numbering system?

The model of the universe that works better in nature is that everything starts at infinity and counts backwards.

It is zero that is impossible, but in decimal terms, you are just accounting for the absence of an integer or "digit" in a column, not an impossibility.

I've only encountered one occasion when I needed complex variables to calculate a potential (convert to electric field). Only used complex variables because the integral couldn't be done using "regular" calculus integration tricks.

Math is good enough that it works. We do have this tiny problem that we do math in a bunch of numbers that we basically just invented. It's not unlike the problem with language- we can't always articulate something new with the old words. Math itself probably isn't flawed for the most part. The engineers view may be good enough: it may not technically be right always, but its so close that it works anyway.

A good example of the problem with using an invented system to describe real phenomenon is to consider what math would have been like before the discovery of zero.

Originally posted by The Vagabond
A good example of the problem with using an invented system to describe real phenomenon is to consider what math would have been like before the discovery of zero.

So math is always in some sort of progress right. But what about the fact that we have been depending on this for so long. If we DO find some flaw in math wouldn't that be a pisser to think that all this time we had been doing it wrong.

It is my personal opinion that all math is seriously flawed.

All math is based upon, a once given measurement that someone somewhere produced and expanded upon.

An example: 1 was decided to be one, but by what constant. There is no constant variable that one was derived from.

Thus 1 is nothing short of a name for an imperfect measurement, integer, variable - whatever.

The reason math works is because we believe it works.

Hence another example:

2>1 To us this would appear true, but in reality what constant value is 2, other than the value we agree to place upon it. Two is an imaginery number; hence this application is only true to us, we understand it and we have created vast abilities from it. But no where in the universe is 2 defined. Thus in reality 2>1 is not even false it's non existent.

Part of this became apparent to me when I got into quantum mechanics; I began to see a sort of blurred vision of what we perceive to be reality.

It became apparent to me that math carries no value; even if modern math were to somehow be based upon a solid measurement like a distance between two steady constant particles, you thus would now have to consider the imperfection of the particle measurement. Hence we would have to recalculate based upon string measurements.

This true concept of math actually lays beyond our means of understanding. We are at best consciously aware of four dimensions but we calculate in only two dimensions yet we strive to perceive nine or higher dimensions.

Hence we only perceive the tip of the iceberg, thus math works because we will it to work.

You see math only exists as a way to organize a chaotic universe. It is our will to organize it, thus just as a tip of an iceberg would bend to our will if we were to utilize a mining of it's surface exterior so does our effect equal in the universe. Our actions do not necessarily demonstrate an absolute of understanding. We can exist on the surface unaware of the universe's sublayer but yet still maintain a control because of our drive to will.

I know many people will disagree with me, but to me it's pretty apparent.

Linear mathematics is a flawed concept, and I think the very exsistance of Pi prooves it. It is literally trying to cram a square peg into a round hole. Our obsession for containment and measurement is useless until we somehow manage to break out of linear mathematics. You come up with some way to mathematically demonstrate this and you would probably be responsible for the next big break through in mathematics, but here is my theory... I found that Eastern Philosophy has touched on some very basic, but important concepts, the here and now, the One-ness of the universe, and the balance of the two forces in the universe. I believe that everything tries to acheive a balance, or a perfection, maybe I would go so far as to say that all matter tries to become spherical, and that 'chaos' is a result of the conflicts in the interraction of matter. That is why we can't come up with a linear solution to Pi, there isn't one. We are locked into a three dimensional thought and with no way to mathematically express either perfection or infinity. Is there some way to express the process of acheiving Pi? I have heard that computer fractals spiral into infinity trying, but perhaps that is the limit of there three dimensional interpretation of the data... Am I making any sense?

Want to see what Pi 'looks' like?
Hook your video camera into your tv sometime and point it at the middle of the screen and watch what happens, what you are seeing is a three dimensional, visual representation of a complete loop in the electromagnetic spectrum.
Feedback in a microphone is an audio representation of the same thing, though it is far less pleasant.

To put it as succinctly as possible, I will rely on Murphy's Laws of Combat.

If it's stupid but it works, it isn't stupid.

agh, this is tedious talk.

Maths is not flawed, in the sense that it is a selfconsistent system of knowledge. In this respect it is no different to any other system of knowledge.

However, and this is personal belief, I think maths is not only not flawed, but is absolute, it is not relative to anything. Mathematical knowledge (as long as it is consistent of course) is fundamentally correct, universally true and has no qualifications. In this sense it is like religion, you either believe it or you don't. Maths requires a very few fundamental beliefs for you to be able to comprehend what is goind on, things like the existence of zero, the successor function and the like. I believe it is correct because it appeals to my intuition, which in the end is what maths is basically about, intuition.

hanburu_juuboku, i don't mean to be rude ot dismissive of your ideas, but you seem to be missing the whole point of mathematics, you also seem to be mixing mathematics up with theoretical physics (my degree course). To argue with a mathematician over the existence of numbers is futile, it is a completely pointless exercise which will not only get you nowhere but eventually drive you crazy. Mathematicians 'believe in numbers' in the same way you believe you exist, how are you going to react if someone told you you weren't real? Mathematicians or people who have a belief in maths no more believe numbers are things that run around than anyone else, but what they do believe is that there proper use and application can unlock fundamental truths about the universe.