Curio: general sign for all elements.

1. Nov 2, 2007

ferman

As we have seen some mathematical sign lately in this group, because I put you in the drawing of the general sign of any element.
You also can see more searching “from zero to infinite, ferman”.
Thank you.

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2. Nov 3, 2007

HallsofIvy

Staff Emeritus
Calling them symbols does not make nonsense anything but nonsense!
$$\frac{0}{0}$$ is NOT 1, it is not defined at all .
$$\frac{\infty}{\infty}$$ is NOT 1, it is not defined at all.

3. Nov 3, 2007

ferman

Well, perhaps is time to change erronous concepts.
"Any element divided by itself gives us the unit 1". If not, these elements aren't equal or equivalent.
It is not correct to explain properties of division with properties of multiplication, we have to do with properties of division.

4. Nov 3, 2007

cristo

Staff Emeritus
You need to look up the definition of division. It's defined for real numbers a,b and c, as a/b=c iff a=bc and b!=0.

5. Nov 3, 2007

HallsofIvy

Staff Emeritus
Yes, let's please change that erroneous concept:

"Any element divided by itself gives us the unit 1" is an erroneous concept. Please change it!

"It is not correct to explain properties of division with properties of multiplication, we have to do with properties of division."
Because you SAY so? Perhaps you should explain what YOUR definition of "division" is.

(Dang, Cristo got in just ahead of me!)

6. Nov 3, 2007

arildno

Okay, let us bear with ferman for a while!

We introduce a mapping from R2 to R called "D", having the basic property of

D(a,a)=1, for all a in R.

That is valid starting point.

What other properties should D have, ferman?

7. Nov 3, 2007

arildno

If "*" stands for multiplication,
should we have the rule D(a,b)=a*D(1,b) for all a and b in R?

8. Nov 3, 2007

Hurkyl

Staff Emeritus
ferman: you can certainly define your own division symbol to have the property that x/x=1 for all x. But that does not guarantee that it has anything to do with division as used by mathematics. (In fact, it guarantees that your definition will be incompatable with most mathematical division operations)

9. Nov 3, 2007

arildno

For other posters:
According to ferman's website, we also have the rule
D(a,D(a,b))=b

Do we have rules like IF D(a,b)=D(a,c), THEN b=c, ferman?

Last edited: Nov 3, 2007
10. Nov 3, 2007

ice109

i don't understand why people do this. attention seeking on the internet, here of all places

11. Nov 4, 2007

arildno

ferman:

Should we have the rule
D(a+b,c)=D(a,c)+D(b,c), that is: $$\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$$?

12. Nov 4, 2007

ferman

Well friends, I think I am right.
To explain my viewpoints, I put you a summary of this question with a drawing (important for comprehension). This you also can see in the end of my web, "fron zero to infinite, of ferman".
---------------
When we operate with empty sets, we usually look on (simple and exclusively) the result of their component elements to which we date as zero when having none.
But we forget something essential, and it is the number of empty sets with which we are operating.
If, as in the drawing, we take an empty glass to which we multiply by 3, the real result will be we have 3 empty glasses, but the partial result will be we have zero elements in these 3 empty glasses.
So, in this case we adjust as result ALONE THEIR ELEMENTS, but we forget we are USING A SERIES OF SETS.
Although this operation method is of great importance due to we later use this property as principle, base and justification of other operations, as can be in division.
And clear, when taking as principle and explanation to a partial result and not to the total result of the operation, because we end up accepting indetermination principles that are not correct.
For example, if we put 1x0 = 4x0 we are accepting that both terms are identical, when they are not because in the first term there is alone an empty set and the second term there are four empty sets, although the number of component elements is same in both term of the equality.
This way, when we operate (3x0 = 0) we should accept that we are operating PARTIALLY and alone with relation to the elements of the empty sets that we are using.
In the same way we should accept that this operation is PARTIALLY UNCERTAIN, since three empty sets cannot be the same thing that an empty set.
For this same reason we cannot use this type of postulates to conclude that 0/0 are an uncertain operation, since their solution is 0/0=1 abiding to the properties of the division.

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13. Nov 4, 2007

arildno

I have asked you several specific questions as to how your "division" interacts with other arithmetic operations, now start answering them.

14. Nov 4, 2007

ferman

Well, this would be the main property of division:
Equivalence principle:

"In any division the dividend contains N times to the quotient, being N the divider."

In this sense, the current conclusion as for 0/0 is uncertain, and so any number could be the result of this division seen to be clearly incorrect. Question that we can see with any example:
If were 0/0 = 7 then we would have that the dividend ( 0 ) should be seven times superior than the divider ( also 0 ) and this is not this way since they are the same one.

15. Nov 4, 2007

ferman

Don't worry, I'll treat to response all them. Time to do.

16. Nov 4, 2007

arildno

Again, mere silly blather about "correctness".

I have already taken into account your desire to have a "D" mapping satisfying the basic principle D(a,a)=1 for all a in R.

What of the other properties I've mentioned does D have?

17. Nov 4, 2007

HallsofIvy

Staff Emeritus
Doesn't this contradict what you initially said, "It is not correct to explain properties of division with properties of multiplication, we have to do with properties of division" since you are now DEFINING division in terms of multiplication?

Now, you are going to have to tell us what you mean by "seven times superior than the divider". I don't believe "superior" is standard mathematics notation.

While I might be getting lost in the grammatical intricacies of "so any number could be the result of this division seen to be clearly incorrect" (isn't there a verb missing from this clause?), if I am interpreting this correctly you seem to be now agreeing with what I said and contradicting the assertion on your website that 0/0= 1.

18. Nov 4, 2007

arildno

Besides, 0=0+0+0+0+0+0+0=7*0, that is, 0 IS 7 times "superior" than itself..

19. Nov 4, 2007

ferman

Well, perhaps I find very complicated some of your questions.
My rule or main property of division is very easy:
Given a, b and c that can be any type of number (or elements) the division a/b=c is correct "when a contain b time to c".

6/3=2 6 contains 3 time to 2
8d/2=4d 8d contain 2 time to 4d
d/4 = h d contains 4 time to h
S/1 = S S contains 1 time to S

Now well, when is the same o equivalent element that is divided by the same one, we obtain the pure unit without no one type of qualification.

6/6 give us 1
0,01/0’01 give us 1
h/h give us 1
@/@ give us 1
x/x give us 1

All this propitiated by the commutive property of division (second property): " En any division we can change the dividend by the quotient being also fulfilled the new resultant equality"

6/3=2 --------- 6/2=3
S/1=S --------- S/S=1

Sorry for not understand well your other proposals.

20. Nov 4, 2007

arildno

As I have already stated, you wish D to have the property D(a,D(a,b))=b.

Fine. You are entitled to that. Now go on.