Classification of zero and 0

[arkain101]

In another topic I was intrigued to ponder some thoughts on mathamatics.

But since this particular topic is getting old I thought I would create a new one as to get it out of the hole of lost topics.

A person was mentioning a dilemma in math with 0.

jonorr wrote:
Now I am going to prove something that was available to mathematicians even in Al-Khwarizmi's time, but some how went unnoticed.

Let x and y be equal, non-zero quantities
x = y
Add x to both sides
2x = x + y
Take 2y from both sides
2x - 2y = x - y
Factorise
2(x - y) = x - y
Divide out (x - y)
2 = 1.

This amazing result shows that 2=1, and by subtracting one from each side we have the even more amazing 1 = 0! With this in mind it is immediately obvious why dividing by zero is acceptable, because it's really the same thing as dividing by 1.
But just to be sure this is ok, let's test it out. Remember earlier when I talked about dividing zero marbles into zero marbles? Well since we now know that 0 = 1, lets plug this in and see what we get.

0/0 = 1/1 = 1

That aside I will paste here some analizations I made that seem to clear up this and possibly other problems.

I wish I could write it out with a more advanced and educated looking post, but since math is not an area i have alot of experience with i guess it'll have to do.

Zero is not really a number. It is not a value. It is a shape that represents the empty space that would otherwise be in an equation. You could replace 0 with the drawing of infinity (sideways 8) and say, this is symbol represents what we must call a non-value. Either infinite or nothing, both are the same.

Zero/0 is not the same as having a number containng a 0 such as fifty - "50" that has a similar shape in its symbol.

In my opinion zero is not properly represented with the symbol of 0 and causes confusion (maybe not for all but for of course some). It should not actually be represented in the classifcation of what we call a numbers or digit symbols that represent value, which of course are 1,2,3,4,5,6,7,8,9. Where decimal place representation of 0 which is not "zero" but instead is and should be called something along the lines of adecimal place symbol.
As far as I know in basic math, in the symbol of this kind of number representation they (the only nine numbers/symbols of value 1,2,3,4,5,6,7,8,9) are the symbols of value. But zero-0 is not a number of value and is not a number period (in terms of number meaning symbol and value) but on the contrary a word or symbol for lack there of such value, quantity, existence.

I am curious what some of you think on this.

0/0 is as much the same as saying gasdfasd/gasdfasd. It is not a value and is not a number in the sense of which 1-9 are numbers / symbols.

We should find a new way of representing the symbol of nothing/zero. The infinity symbol for example.

your thoughts?

BTW, I have a question. What is this symbol type called that uses 12456789? We have what we call english, metric, standard, french etc.. but what is this type of numerology? if that is the correct phrase.

[kamil]

The proof that 2=1 has a flaw in it.

Look at the first assumption that x=y, now look at the conclusion 2(x-y)=(x-y)

it means that: 2(x-x)=x-x

so: 2*0=0

But dividing 0/0 doesnt necesarily equal 1.

Sorry arkinain, i didnt read the rest of your post because i was amazed by this.........but i promise to read it later

[C1ay]

Originally Posted by MathWorld

Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is neither negative nor positive. A number which is not zero is said to be nonzero. A root of a function f is also sometimes known as "a zero of f."

More....

Is there a reason I shouldn't move this to "Strange Claims"?

[Qfwfq]

I was wondering that myself. Only now I searched for the quoted post and it doesn't look as if jonorr meant it seriously.

How seriously do you mean to be, Arkain?

[arkain101]

fire it over there.

I am serious. The 0 symbol has more than one meaning and could be re-written different ways.
I didnt realise the jonorr post was not serious I thought he was quoting from the book, the final theory.

[pgrmdave]

The jonorr post is erroneous, due to the point at which he divides both sides by zero. Since it is impossible to do this, the answer he receives is incorrect, and the conclusion he arrives at is wrong. Remember, dividing can be thought of as putting a large group of objects into multiple smaller groups of objects and then counting the number of groups. Let's use the equation 10 / 2 = 5. So lets say we have ten buttons - we need to put them into as many groups of two as we can, so we start seperating them, and when we finish, we have five groups. Now, we try a similar thing but with 10 / 0 = ? So, we take our ten buttons and we make a group of zero - Hey! That was easy, we didn't need to do anything! So, we make another group of zero, and another, and another... we could potentially do this infinitely, and so dividing by zero will never provide you with an exact, correct answer, it is undefined.

And I believe our number system is arabic.

[Pyrotex]

Originally Posted by arkain101

In another topic I was intrigued to ponder some thoughts on mathamatics....your thoughts?
BTW, I have a question. What is this symbol type called that uses 12456789? We have what we call english, metric, standard, french etc.. but what is this type of numerology? if that is the correct phrase.

Arkain,
the set of symbols we use for our numbering system, 0123456789 (don't forget the zero!) is called the Arabic system. The 'zero' symbol may have come from India, but the Arabians adopted it and investigated it in their treatises on math and algebra.

The problem with this post stems from the following words:
"we have the even more amazing 1 = 0! With this in mind it is immediately obvious why dividing by zero is acceptable, because it's really the same thing as dividing by 1."

This is known as the "Big Lie". The erroneous result makes it obvious why dividing by zero CANNOT be acceptable. And it could NOT be more clear that dividing by zero is NOT the same thing as dividing by one. Dividing by one does NOT give us erroneous results.

0*X = 0*Y is true for all X and Y.

If dividing by zero were legit, then X=Y is proved for all X and Y. Ridiculous.

Zero is a number, plain and simple. It is just as much a number as one is. All arguments to the contrary are bafflegab.

[InfiniteNow]

Interestingly, while still in college, I had a thought that zero equals one and that they both equal infinity. I might have been high though... Yeah, I'm about to get my ass handed to me by a bunch of mathemeticians for that last statement, but I like the romance of bringing the three together in this manner...

Read a cool book on the history of zero called "The Nothing that is." For ages, we had concepts in mathematics to represent something, but not the absence of something. Okay, I hate it when I ramble.

[Pyrotex]

Originally Posted by InfiniteNow

...but I like the romance of bringing the three together in this manner... Okay, I hate it when I ramble.

I love it when you ramble.

You want a truly amazing piece of math that will rock your universe?

e^(i*pi) = -1

e is the base of the natural logrithms: 2.781828....
pi is the ratio of circle circum/diam: 3.14159....
i is the square root of minus one!!!!

you've got two transcendentals, exponentiation, an imaginary number, a real integer and negation all in one formula. What more do you want? Chocolate sprinkles?

A clue as to how this works is e^(c) has an expanded solution base in the complex plane equal to sin(c) + i*cos(c)

Plug (i*pi) in for c and you have i*sin(pi) + i^2*cos(pi)
= (i)*(0) + (-1)*(1) = -1

[InfiniteNow]

Does this work out properly? I'm getting that i = sq.rt of -1 AND i^2 = -1...


square root of [e^(i*pi)] = i.

Hence, i^2 = e^(i*pi)

and i^2 = -1?