Mathematics Is Wrong. Here's Why.

reply to post by MathiasAndrew


I have the Oxford English Dictionary upstairs if you want to borrow it.

You keep saying this:

* = x
+ = -

But, these two expression aren't the same. In the first one, you have two operators that describe the same thing... both * and x signify multiplication. In the second, you have two that are reciprocals... + being addition and - being subtraction (of course).

So, what's your point?

reply to post by CLPrime


Does this do: reciprocal

1 divided by a number (any number)

eks.
The number: 2

its reciprocal: 1/2

The reciprocal of 2 is 1/2 = 0.5

The reciprocal of 0 is undefined. Its a complex infinity.

reply to post by spy66


I was also looking for the reciprocal of an operator, but it doesn't matter anymore, 'cause I've gone another route.

reply to post by CLPrime


You're correct trying to type out the equation i made a mistake in the notation.

I used * when i should have used /

I can see where you were confused by my mistake.

Let me rewrite it

100 / 0 = 100 * 0

100 + 0 = 100 - 0

Thanks for pointing that out

Alrighty, so...

Originally posted by MathiasAndrew

100 / 0 = 100 * 0

100 + 0 = 100 - 0

Now, way back on page 21, you said:

Do you understand reciprocals? Here is how you solve the equation 100 x 0 =

the 0 and the = sign are canceled

if you like you can move the zero to the other side of the equals sign like this 100 x0 = /0

But you forgot the last step in this mathematical equation, which is to now cancel out the 0 and the equals sign

Problem solved

You forgot that there is an invisible divide by zero on the other side of the equals sign the x 0 and / 0 cancel each other

And, on the following page, you said (with the sign fixed):

100 x 0 = ... should look like this 100 x +0 = / -0

100 / 0 = .. should look like this 100 / +0 = x -0

the zeros cancel each other out and you're left with 100

I think the confusing part is that, while you may know what all of this means in your own head, it's hard for the rest of us to know what you mean. Look at the operators for a minute. You have multiple operators in a row, and no mathematician will ever say that makes sense. It may be "5th grade algebra," but it's not the way any 5th-grader would write it or ever be able to understand it.

So, with that in mind, can you describe what you're trying to get across in words? Please?

Originally posted by MathiasAndrew
reply to post by CLPrime

 

You're correct trying to type out the equation i made a mistake in the notation.

I used * when i should have used /

I can see where you were confused by my mistake.

Let me rewrite it

100 / 0 = 100 * 0

100 + 0 = 100 - 0

Thanks for pointing that out

Wow guy way to create an impossible math problem 0 is not undefined in the equation 0 has a value you cant treat it like x. If your going to make a point at least try to use math!

reply to post by CLPrime


What I was trying express is that when solving the equation 100 x 0 =

You can not simply apply the action of the operator

You must insert the reciprocal operator on the other side of the equals sign and then simplify

I was trying to convey the fact that positive and negative numbers can cancel each other out also,

but I made a mistake by doing it that way and should have written it like this

100 x 0 = 100 / 0

100 + 0 = 100 - 0

reply to post by dragonridr


This is the way that math solves the equation 100 x 0 =

and conversely how it solves the equation 100 / 0 =

How else do you arrive at the correct answer?

Which is 100

Originally posted by MathiasAndrew
reply to post by dragonridr

 

This is the way that math solves the equation 100 x 0 =

and conversely how it solves the equation 100 / 0 =

How else do you arrive at the correct answer?

Which is 100

Division by zero is undefined, therefore 100(0) cannot equal 100 / 0. 100 / 1 = 100, because 1(100) = 100. However,100 / 0 is undefined because for 0(x) = 100, x cannot be solved.

Originally posted by MathiasAndrew

I was trying to convey the fact that positive and negative numbers can cancel each other out also ...

100 x 0 = 100 / 0

100 + 0 = 100 - 0

This is actually not the case. Multiplication is short-hand for addition, and the characteristics of the addition operator don't carry over.
In the case of addition:

100 + n = 100 - (-n)

0 is neither positive nor negative, so we can ignore its sign:

100 + 0 = 100 - (-0)
100 + 0 = 100 - 0

In other words, the additive reciprocal (such that the additive reciprocal of a is -a) of 0 is itself - that is, a = -a, and a = 0. Therefore:

100 + 0 = 100 - 0

This doesn't work, however, with multiplication. In this case, we have to look at the multiplicative reciprocal (such that the multiplicative reciprocal of a is 1/a):

100 x n = 100/(1/n)

In this case, a = 1/a, and the only number for which this is true is 1. Therefore, 1 is its own multiplicative reciprocal.

There is only one number that has itself as an additive reciprocal - 0.
There is only one number that has itself as a multiplicative reciprocal - 1.

100 x 1 = 100/(1/1)
100 x 1 = 100/1

This doesn't follow for 0, because 0 is not its own multiplicative reciprocal.

We can actually prove that 0 is not its own multiplicative reciprocal.
For 0 to be its own multiplicative reciprocal, 0 would have to equal 1/0. That is,

0 = 1/0

And, I know that's exactly what this thread is suggesting. So, bear with me.
Let's look at the graph of 1/n:

[atsimg]http://files.abovetopsecret.com/images/member/1f828e174cea.png[/atsimg]

The horizontal asymptote of the graph is 0 - that is, the limit of 1/n as n goes to both positive and negative infinity is 0.
The vertical asymptote of the graph is undefined - that is, the limit of 1/n as n approaches 0 from either side is a little iffy. From the left, 1/n goes to negative infinity; from the right, 1/n goes to positive infinity.

And this is where the subject blends with what the OP was saying. What this seems to suggest is that, at 0, the graph is at both negative and positive infinity - and, presumably, everywhere in between.
So, this is actually our definition of 1/0: it is the set of all Real numbers. Not any particular number, but all of them, simultaneously.

On the other hand, 0 is the exact opposite. 0 is defined as a null set.

1/0 is the set of all Real number.
0 is an empty set.

These two are mutually exclusive. Therefore, 1/0 cannot equal 0, and, therefore, 0 is not its own multiplicative reciprocal.

Originally posted by MathiasAndrew
reply to post by dragonridr

 

This is the way that math solves the equation 100 x 0 =

and conversely how it solves the equation 100 / 0 =

How else do you arrive at the correct answer?

Which is 100

I just came here to make an interjection. Perhaps this conversation can be made more clear by referring the the field axioms and thinking about what operations multiplication and division denote. Multiplication can be made clear made clear by thinking of it as repeated addition, and division repeated subtraction. But for division you cannot divide by zero because of the field axioms and properties of the number zero.

I'll give a hint.

b / a is defined to be a number z such that z*a = b. What happens if a becomes 0? Also is 0 a unique element in the set of real numbers? a*0 means that you add 0 a times and also a 0 times because of the associative laws that people learn in elementary school when dealing with numbers.

Hope this makes it clear to some people, Maybe from here we can go to the difference between finite and infinite.

So perhaps if you want to make new claims you have to redefine the rational operators to make it consistent with your new math system. So start at a definition level and build up. Good luck!


EDIT: I can finally see what you are trying to say though. But then you are thinking of multiplication and division at a difference sense that people are used to. Again, you have to define what the operators mean. Also what does 100*1 and 100/1 mean, and is 1 therefore the same as 0?

This is an interesting topic because it goes into the foundations of analysis.

I'd like to add that if you accept the notion that

a/0 = infinity

then algebraically,

0 * infinity = a



So you can see the dominant nature of infinity. Infinity cannot be made nothing but nothing can be made infinity.

Originally posted by CLPrime

Originally posted by MathiasAndrew


The horizontal asymptote of the graph is 0 - that is, the limit of 1/n as n goes to both positive and negative infinity is 0.
The vertical asymptote of the graph is undefined - that is, the limit of 1/n as n approaches 0 from either side is a little iffy. From the left, 1/n goes to negative infinity; from the right, 1/n goes to positive infinity.

And this is where the subject blends with what the OP was saying. What this seems to suggest is that, at 0, the graph is at both negative and positive infinity - and, presumably, everywhere in between.
So, this is actually our definition of 1/0: it is the set of all Real numbers. Not any particular number, but all of them, simultaneously.

Good work CLPrime

So as you can see, infinity will do well in 0's place.

Originally posted by smithjustinb

0 * infinity = a

And, to illustrate just how interesting a concept this is:

Imagine a line with 0 thickness and 0 height, making it 1-dimensional. If that line is infinite in length (which it has to be, otherwise it's a line segment), then it actually has a real volume - and that volume can be any number. In fact, you can say that the value of the line's volume is every Real number simultaneously.

Specifically the volume of the line is given by:

V = height x width x length (for a rectangular cross-section); or
V = pi x radius squared x length (for a circular cross-section)

In the first case, both the height and width are 0, making their product equal to 0.
In the second case, the radius is 0, making the product of pi and the radius squared is equal to 0.

For both, this leaves:

V = 0 x length

And given an infinite length:

V = 0 x infinity

Which, as I showed, has the possibility of being any Real number - that is:

V∈R

So, counter-intuitively, an infinite, 1-dimensional line has a real volume.

reply to post by CLPrime


volume is l*w*h which only applies to 3d objects

area is what is l*w which applies to 2d objects

length is what is L which applies to 1d objects

you don't multiply by zero, you just remove the dimension from the equation.

A true line can't be any particular length because at the point of defining its length, it becomes a line segment.

A single point which has no length, width, or height, is so indeterminable that it doesn't even exist, yet it does exist as something that is an infinitely indeterminable quantity.

If this thing has no dimensions yet is quantifiable as existing, then this is a paradox. It both exists and doesn't exist at the same time.

It exists because it exists. It doesn't exist because there is no way to measure something that has no dimensions.

As you can see, this is the point where mathematics loses its purpose and no longer applies, yet this single point is just as much a part of our reality as anything else, so that just tells you that math can't do everything.

However, if you want, you can associate a symbol with this mathematical uncertainty, but make it clear that this symbol has no conventional mathematical meaning except to be a symbol from which quantitative analysis can begin as a point to ascend into mathematical dimensions. Yes, this mathematical uncertainty can be said to not exist dimensionally, but rather it exists as existing.

There is already a symbol which applies to this understanding, and it looks like a sideways 8.

Originally posted by smithjustinb

volume is l*w*h which only applies to 3d objects

area is what is l*w which applies to 2d objects

length is what is L which applies to 1d objects

you don't multiply by zero, you just remove the dimension from the equation.

I know the difference between volume, area, and length for 3-, 2-, and 1-dimensional objects. When you remove a given term (width, height, length) from the equation, you remove a dimension entirely. I was establishing the volume of a 1-dimensional object. While this may seem counter-intuitive, I showed that such an object does, in fact, have a real-valued volume.

If you just remove width and/or height from the equation, the you're no longer talking about volume. But, since I wanted to talk about volume, the volume equation has to be left intact, with all three terms.

So, no, for what I wanted to do, you don't just remove the term(s)/dimension(s) from the equation. You have to multiply by 0. That was the basis of my whole point.

Originally posted by CLPrime

Originally posted by smithjustinb

volume is l*w*h which only applies to 3d objects

area is what is l*w which applies to 2d objects

length is what is L which applies to 1d objects

you don't multiply by zero, you just remove the dimension from the equation.

I know the difference between volume, area, and length for 3-, 2-, and 1-dimensional objects. When you remove a given term (width, height, length) from the equation, you remove a dimension entirely. I was establishing the volume of a 1-dimensional object. While this may seem counter-intuitive, I showed that such an object does, in fact, have a real-valued volume.

If you just remove width and/or height from the equation, the you're no longer talking about volume. But, since I wanted to talk about volume, the volume equation has to be left intact, with all three terms.

So, no, for what I wanted to do, you don't just remove the term(s)/dimension(s) from the equation. You have to multiply by 0. That was the basis of my whole point.

Oh sorry, I misundertood you.

I'm not meaning to insult your intelligence if I was.

So basically, you're saying 2 or 1 dimensional objects cannot exist from a 3 dimensional perspective?

Originally posted by smithjustinb

Oh sorry, I misundertood you.

I'm not meaning to insult your intelligence if I was.

No problem. What I wrote was actually something that had literally just occurred to me, so it may have been unclear. I was really just thinking out loud, so I make no claim of its coherency, or its accuracy for that matter.

So basically, you're saying 2 or 1 dimensional objects cannot exist from a 3 dimensional perspective?

I'm saying that, if a 1-dimensional object is infinite in length, then its infinite nature gives it volume just like a 3-dimensional object. I guess you could say that even though it has no width or height, it has so much length that that single infinite dimension causes it to act as if it has width and height.

Spy66 and co, check out this new thread i made, it's in relation to math, it could be wrong or right.
Take a look .

www.abovetopsecret.com...

What's interesting is that computers have special circuitry to handle the number ZERO.

Or more specifically, special circuitry is added to cause an error condition if you try to divide by zero. With out this circuitry, a computer will say that 5 / 0 = 5. Personally I agree with the computer, to me that to divide by zero means to NOT do any division, a do nothing operation. Same as 8 x 0 = 0, which means don't do any multiplication.

Also, without special circuitry, computers treat zero as the beginning point of a vector (or the end depending on your perspective) rather than the connecting point between two vectors (one vector going positive and the other one negative).

To demonstrate let me use the analogy of two buckets. Bucket "A" holds negative quantities, bucket "B" holds positive quantities. Without the special circuitry a computer will treat them as two separate containers. And as separate containers, they each have their own zero point. Bucket "A" has -0 (i.e., negative zero). Bucket "B" has +0 (i.e., positive zero).

To the computer there are two separate vectors (two containers), each with its own zero point. Whereas for us humans, we join the two vectors and ignore one of the zeros, and then state that there is only one zero. Computers require special circuitry, or the programmer has to write special code to convert any results that end up with -0, to +0.

If you think about it, we have it wrong and the computer does it right. You can take a quantity of something and move it from one place to another, bucket "A" to bucket "B". But you can NEVER subtract something from nothing.

0 minus 5 is not possible, there is no such thing as less than zero.

Also, to a computer without special circuitry or programming, fractions don't exist either. Without special programming, when you feed the number 1/3 into a computer it views it as 1 of something, where it take three of them, to equal one of the other. Confused? That's ok, I'm just splitting hairs now. Ha ha, splitting hairs... :-)