Are there any Flaws in Math?

I was in my math class this morning thinking about different things and I came upon this: I wonder if there are any actual flaws to math? Cause I have seen that other post about .99999= 1 and I would like to know if anything like that is true. Also I can't remember who posted this a way long time ago but someone here said that there is a reason why we can't find pi because of some flaw in mathmatics. I always thought it was because there were no straight lines or accurate ways to measure. Well if anyone could help me with this I would greatly appreciate the favor.

Originally posted by The_Final
I was in my math class this morning thinking about different things and I came upon this: I wonder if there are any actual flaws to math? Cause I have seen that other post about .99999= 1 and I would like to know if anything like that is true. Also I can't remember who posted this a way long time ago but someone here said that there is a reason why we can't find pi because of some flaw in mathmatics. I always thought it was because there were no straight lines or accurate ways to measure. Well if anyone could help me with this I would greatly appreciate the favor.

.999999999-repeating, in that sense, is from an asymptote (sp?). Basically, it's an equation where the value will always grow, but never reach one. But in all practical uses, you may as well treat it as 1 since the difference would be negligible and not affect your result in any appreciable way, and it's easier to work with 1 than to work with .99999999999999999

As for pi, it'll be easier if you just look here

[edit on 4-13-2005 by Esoterica]

Pi is a number that is known, but that does not mean it has to conform conveniently to a finite set of decimal digits.

In my opinion there are not necessarily "flaws" in math, except in the logic that you cede when you agree with a proof that 2 = 1.

There are, however, plenty of things that may appear in nature but are not conveniently described by math... irrational numbers and numbers outside the real domain amongst them.

What is the square root of minus seven, anyway?

nothing comes to mind.

a little searching....

Godel book

Originally posted by Dulcimer
nothing comes to mind.

a little searching....

Godel book

Thanks I am going out probably later tonite to pick it up.

Originally posted by MaskedAvatar
Pi is a number that is known, but that does not mean it has to conform conveniently to a finite set of decimal digits.

In my opinion there are not necessarily "flaws" in math, except in the logic that you cede when you agree with a proof that 2 = 1.

There are, however, plenty of things that may appear in nature but are not conveniently described by math... irrational numbers and numbers outside the real domain amongst them.

What is the square root of minus seven, anyway?

2.6457513110645905905016157536393i

Is it true that Albert Einstein didn't believe 3 wasn't a number or something? Also, that dang Pi it never ends, makes me so angry! I hate Pi!

Originally posted by CPYKOmega

Originally posted by MaskedAvatar
Pi is a number that is known, but that does not mean it has to conform conveniently to a finite set of decimal digits.

In my opinion there are not necessarily "flaws" in math, except in the logic that you cede when you agree with a proof that 2 = 1.

There are, however, plenty of things that may appear in nature but are not conveniently described by math... irrational numbers and numbers outside the real domain amongst them.

What is the square root of minus seven, anyway?

2.6457513110645905905016157536393i

I thought you couldn't have square roots of negative numbers like the square root of negative one is i right? So why would any other negative number have an answer?

Aha, we have found a gufflaw.

Since there is no real number whose square is a negative number, it is sometimes said that the square root of a negative number does not exist. However, an expression under a square root sign may take on negative values. While the square root of a negative number cannot actually be found, it can be indicated.

The indicated square root of a negative number is called an IMAGINARY NUMBER. The square root of minus seven is said to be imaginary.

*No. He's real! It's real! Santa Claus is real! *

Originally posted by Enigmatic_Messiah
Is it true that Albert Einstein didn't believe 3 wasn't a number or something?

If this is true it has to be the wierdest thing ever lol. I don't believe this to be true though although I don't exactly know. I will look for it though.

Originally posted by MaskedAvatar
Aha, we have found a gufflaw.

Since there is no real number whose square is a negative number, it is sometimes said that the square root of a negative number does not exist. However, an expression under a square root sign may take on negative values. While the square root of a negative number cannot actually be found, it can be indicated.

The indicated square root of a negative number is called an IMAGINARY NUMBER. The square root of minus seven is said to be imaginary.

*No. He's real! It's real! Santa Claus is real! *

Very true. Imaginary numbers, represented as "i" are needed for certain mathematical problems. Funny though... seeing as they don't even exist.

[edit on 4-13-2005 by CPYKOmega]

Theirs flaws in everything mate! Nothing is perfect! Not even this website (No Offense).

I understand that their are flaws in everything I would just like to learn these flaws lol. I too will admitt that there are flaws on ATS but that is fixable since they can update the site, but would an "update" in math be able to fix the problems?

I am very happy you made this post and that I was able to respond before it grew to like 4 pages. In a very simple answer regarding whether math itself has any flaws, the answer is NO. This DOES NOT mean that math is perfect in what it is trying to describe, but the way it all works out is that math itself is perfection as we have invented it. Math was originally based on a euclidean intellect. Lets remember that when people like einstein and minkowski and newton and the such derive new theories, they also derive new equations based on the same mathematical framework layed out by the earliest mathematicians.

This lends to the nature of increasing proofs and the such. So, back to relations, for example, 2+2 must always be 4, but the number 4 itself is not related to whatever 4 really is regarding what your describing as 4 pieces of pizza (heres where philosophy comes in handy). We only see 4 peices, but why cant we see 8 or 10 or 12. Math is describing how we see 4. Math was derived to describe how what we observe works. Calculus was invented to describe objects in 3-d motion and volumes etc. These calculations have been proven beyond belief. Therefore, the math is perfect within itself, but it is possible, very possible, that the truth of what is being described is falsely related to math. Did I say all that right? So finally, what i'm trying to say is that, math is here to tell us how something we observe works, moves or changes. If our observations are wrong, then math is wrong. Even einstein found no flaws with math, he only expanded it. Maybe somebody with better writting can help me convey this. By the way, I have gone very high into mathematics as a student.

Train

Oh the flaws of maths.... I dont think there are really many flaws with maths, however I feel they are more with the equations we use.

I once read somewhere, could have been here, that when an equation is discovered, whats there to say that there are not hidden values, so munute (sp) that cancle that were not included. If that didn't make sence here is an example.

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.

Math has many paradoxes, I wouldn't call them errors. Look up Toricelli's Trumpet, it's a pretty cool paradox (assuming you know Calculus II, otherwise you may not know the math, but you'll definitely understand the outcome).

By the way, imaginary numbers are useful because sometimes when manipulated they produce real numbers. Although the subject of Complex Variables itself really sucks. I hated that course, it was the hardest math course I've ever taken.

Originally posted by MaskedAvatar
Aha, we have found a gufflaw.

Since there is no real number whose square is a negative number, it is sometimes said that the square root of a negative number does not exist. However, an expression under a square root sign may take on negative values. While the square root of a negative number cannot actually be found, it can be indicated.

The indicated square root of a negative number is called an IMAGINARY NUMBER. The square root of minus seven is said to be imaginary.

*No. He's real! It's real! Santa Claus is real! *

It has always been a challenge to me to imagine that a complex number (that is, a combination between an imaginary number - a mutliple of i - and a real number) is only one number, but it still has 2 dimensions!

Is that a clue to our multi-dimensional model of space? As, so far in classic physics, and as far as I know, mostly in quantum, we need 3 numbers to represent a place in space, that would explain some things... In a complex numbers world, that would be enough to have 6 dimensions... Or am I completely wrong?

I always thought that in order to pin-point a place in space you need 6 co-ordinates....

as for complex numbers, what does the 'i' stand for :| I know its something you sub in when deviding a negative number :S

Originally posted by racos
I always thought that in order to pin-point a place in space you need 6 co-ordinates....

as for complex numbers, what does the 'i' stand for :| I know its something you sub in when deviding a negative number :S

Well, as far as I know (knew?), a place in space is 3 coordinates: x, y and z, or otherwise length, width and height, in any order...

In complex numbers, the i stands for 'imaginary'. i is supposed to be the square root of -1, as stated above. Therefore, the i component of a complex number is called the imaginary component (at least in French... )

What space that you thought of would need 6 coordinates?

I know what you're trying to say, and you are incorrect in your thinking of it. It's hard to type out mathematics...wish I could explain it in person with a piece of paper.

The subject of complex variables isn't that complicated (unless you had a professor like I did who enjoyed making tests absurdly difficult), mostly what I take out of it as a physicist is that you can produce a real number out of imaginary numbers. It's used alot in higher level physics courses like EM theory and Quantum.