Curio: general sign for all elements.

[arildno]

Again, I ask you:
What other properties than D(a,a)=1 and D(a,D(a,b))=b for all real a,b would you like your "division" operation to have?

 

[d_leet]

Again, I ask you:
What other properties than D(a,a)=1 and D(a,D(a,b))=b for all real a,b would you like your "division" operation to have?

To ferman

You should note that if you also wish to have the property that 0/a is 0 for all nonzero a then the two properties that arildno mentions above are not consistent because then if we take any nonzero b we would have

D(0,b)=0
and
D(0,D(0,b))=b
BUT
since D(0,b)=0
we have that D(0,D(0,b))=D(0,0)=1

And thus if you wish to have the three properties

1). 0/a=0 for all nonzero a
2). D(a,a)=1 for all a
3). D(a,D(a,b))=b

These imply that for all nonzero b, b=1.

 

[arildno]

I was sort of waiting for him to fall into that little trap..

 

[Moo Of Doom]

And thus if you wish to have the three properties

1). 0/a=0 for all nonzero a
2). D(a,a)=1 for all a
3). D(a,D(a,b))=b

These imply that for all nonzero b, b=1.

I'm under the impression, that he would reject (1). He has said that N*0 = 0 is only "partially" true, and thus 0/a = 0 probably only "partially" holds. It is a bit hard to decipher his ramblings, though...

 

[d_leet]

I'm under the impression, that he would reject (1). He has said that N*0 = 0 is only "partially" true, and thus 0/a = 0 probably only "partially" holds. It is a bit hard to decipher his ramblings, though...

Yea that is probably true, but then he can't be willing to accept that a+0=0+a=a for all a anymore, so he needs to redefine the properties of zero, and of the arithmetic structure of his whole system in order to tell whether or not it is consistent with itself and what he wants it to do.

 

[ferman]

A.-
0/a = 0 is not mine. I put this because it is accepted in mathematics.
Really, and as I understand, this is acceptable in pure mathematics, but some debatable in mathematics of sets.
For example,
--if I have 3 empty sets 0+0+0 y can divide it by 3, getting 1 empty set 0.
--if I have 1 empty sets 0 y can divide it by 2, getting ½ of empty set.
But this question is very confuse to treat it now, and not important.
B.-
The only two question that I expose here are:
1.- a/a = 1 -- from equivalence principle.
2.- We can change dividend by quotient and obtain a NEW equality. So a/a = 1 give us a new equality when the change a/1= a. But this is a new equality where a doesn’t have to be equal to 1.
This property (I call commutive) and it is also given in subtraction.
Other question.-
Sorry for not use expressions as D(a,D(a,b))=b but I am same aged and don’t have accustomed to use them.

 

[arildno]

It is you who are confused, not us.

 

[Integral]

Shades of the Theory Development forum.

Personal theories are not allowed topic of conversation. IF this is not a personal theory then what is?

Thread locked.