Philosophy Now Forum

Hobbes' Choice wrote:

conway wrote:As an addition to all current field axioms


"For every A in S there exists a z1 and a z2 constituting A, such that any A in operation of multiplication or division is only representing z1 or z2 in any given equation. Such that z1 for all A's other than zero equal A. Such that z2 for all A's other than zero equal A. Such that z1 for zero equals 0. Such that z2 for zero equals 1."

Only on Thursdays.

Twice on Sunday.

Dalek Prime wrote:

Hobbes' Choice wrote:

conway wrote:As an addition to all current field axioms


"For every A in S there exists a z1 and a z2 constituting A, such that any A in operation of multiplication or division is only representing z1 or z2 in any given equation. Such that z1 for all A's other than zero equal A. Such that z2 for all A's other than zero equal A. Such that z1 for zero equals 0. Such that z2 for zero equals 1."

Only on Thursdays.

Twice on Sunday.

But only if there is an "R" in the month

I am very bad at interpreting sarcasm....if an insult is intended, I am afraid that a more direct approach is necessary. Any real desire to discuss my post and it's link to the original post? Or do you guys prefer to stay off topic?

conway wrote:I am very bad at interpreting sarcasm....if an insult is intended, I am afraid that a more direct approach is necessary. Any real desire to discuss my post and it's link to the original post? Or do you guys prefer to stay off topic?

Your post is meaningless, as you well know.

That is certainly not what I think. I will offer pure mathematics.

z1 for 0 = 0
z2 for 0 = 1

z1 for A = A
z2 for A = A


0(z1) x A(z2) = 0
A(z2) x 0(z1) = 0

A(z1) x 0(z2) = A
0(z2) x A(z1) = A

Consider z1 as value and z2 as space for any given number. Naturally division is the inverse, without being commutative. That is z1 is always first z2 is always second. So that


A(z1) / 0(z2) = A
0(z1) / A(z2) = 0

conway. The criticism of your post was that it was meaningless and your mathematical elaboration of it has done nothing to void that criticism. What does it mean?

Leo

I understood the quite clear criticism of the "meaningless" of my post. As it came after my request for clarification as to the sarcasms in their reply's to my original post. If you do not already "inherently" understand what I have already posted then either....

1. it is wrong....but not meaningless
2. or you just don't understand


In any case thank you for your time.

Am I to assume that you cannot translate your obscure message into the vernacular so that a simple country lad like me might be privileged to share in the wisdom of it? If so what the hell are you doing in a philosophy forum?

conway wrote:That is certainly not what I think. I will offer pure mathematics.

z1 for 0 = 0
z2 for 0 = 1

z1 for A = A
z2 for A = A

Okay, let's start here.
Why, how and so what?

Leo, Hobbs

Very well we can take the pure philosophical route.

I am saying the following.....

1. Division by zero is definable
2. There are varying quantities of zero.
3. The space of zero is not equivalent to the value of zero.
4. The space of zero is equivalent to the space of 1.


And as a link to the original post.

The commutative property of multiplication does not really exist. It is that multiplication is RELATIVE to what "symbol" is declared as space and what symbol is declared as value, in any equation.


0(as value) x A(as space) = 0( as a number)
A(as space) x 0(as value) = 0(as a number)

0(as space) x A(as value) = A(as a number)
A(as value) x 0(as space) = A(as a number)

conway wrote:Leo, Hobbs

Very well we can take the pure philosophical route.

I am saying the following.....

1. Division by zero is definable
2. There are varying quantities of zero.
3. The space of zero is not equivalent to the value of zero.
4. The space of zero is equivalent to the space of 1.


And as a link to the original post.

The commutative property of multiplication does not really exist. It is that multiplication is RELATIVE to what "symbol" is declared as space and what symbol is declared as value, in any equation.


0(as value) x A(as space) = 0( as a number)
A(as space) x 0(as value) = 0(as a number)

0(as space) x A(as value) = A(as a number)
A(as value) x 0(as space) = A(as a number)

What do you mean "zero"?

conway wrote: Very well we can take the pure philosophical route.

I'm pleased to hear it. Mathematical philosophy is a respected branch of the philosophical discourse and an understanding of it is critical to understanding what mathematics can and cannot meaningfully tell us about the nature of physical reality.

conway wrote:1. Division by zero is definable

As what?

conway wrote:2. There are varying quantities of zero.

No there aren't, because zero is not a quantity. Zero is the absence of a quantity because nothing is not something.

conway wrote:3. The space of zero is not equivalent to the value of zero.

What is the space of zero?

Leo

1. I am pleased that you are pleased. I my self prefer philosophy.....it is not however the route one takes with mathematicians. Also I agree.


2. I defined division by zero with a previous eqution....as I recall you labeled the entire post a "mathematical elaboration".


3. Zero is NOT nothing in mathematics. If it were....then you must explain exponents of zero and logarithms of zero. Both that indicate zero is NOT nothing. Besides......I have agreed with many a phd on this particular subject. Zero is NOT nothing.

so what is it......?

4. The "space" of zero is clearly defined on any given number line (1 + (-1) proves this). And it is equivalent to the space of 1. This is no matter the semantics, or symbols, or placement system used in the creation of the number line.


Leo and Hobbs

All numbers can be defined as compilation of two different and distinct things. That is space, and value. So all numbers have space, and have value. So then zero as a number, not "nothing", also has a space and a value.

2 (as a number) = (1 value, and 1 value)...occupying... +... (1 space, and 1 space)
1 (as a number) = (1 value)...occupying... +... (1 space)
0 (as a number) = (1 undefined value)...occupying... +... (1 space)

Put the values into the spaces then add, and you make a number.


So it is that the value of zero is not absent, non-existent, or nothing. But that the value of zero is undefined. The space of zero is defined as 1.






Philosophically speaking, and on a side note.....

"Nothing" does not exists. By definition. Therefore logically one can not use a symbol.....which exists....to represent that which does not exists. Unless you wish to run the risk of error. I mean we "physically" can label an apple with a poison symbol, but we run the risk of error.

conway wrote:
"Nothing" does not exists. By definition. Therefore logically one can not use a symbol.....which exists....to represent that which does not exists. Unless you wish to run the risk of error. I mean we "physically" can label an apple with a poison symbol, but we run the risk of error.

Then you have contradicted yourself, more than once.

Ever heard of null or nil in programming, conway? Are you seriously suggesting something that doesn't exist can't be symbolized or discussed? You clearly have not heard of the non-identity problem, and how it's not a problem at all, but an issue in the arguer's lack of understanding and comprehension.