ajb Posted June 27, 2015 Posted June 27, 2015 If you have 0*A not equal to A*0 then you have a noncommutative structure. This makes division even harder to properly understand. You cannot be dealing with the standard structure of the real numbers.
conway Posted June 27, 2015 Author Posted June 27, 2015 (edited) It is still equal. It is still commutative. This axiom follows after all other axioms. Z1 for 0 = 0 Z2 for 0 = 1 Z1 for A = A Z2 for A = A A does not equal 0 ( 0(Z1) * A(Z1 or Z2) = 0 ) ( A(Z1 or Z2) * 0(Z1) = 0 ) ( 0(Z2) * A(Z1 or Z2) = A ) ( A(Z1 or Z2) * 0(Z2) = A ) Edited June 27, 2015 by conway 1
conway Posted June 27, 2015 Author Posted June 27, 2015 Ahh I see what you are saying ajb. If you will follow the link provided in #17 you will see that there is a group of two sets of axioms. One for addition one for multiplication. I stated in #18 that axioms for addition were kept as well. I however only posted multiplication. 1
ajb Posted June 27, 2015 Posted June 27, 2015 (edited) If you are allowing A*0 = A, then what is A*A-A*A? Do we keep distributivity? Let us assume A-A = A+ (-A) = 0. So we understand the element -A as the additive inverse of A. Then A*0 = A*(A-A)= A. Okay, but A*(A-A) = A*(A + (-A)) = A*A + A*(-A) = A*A - A*A =0, if the usual axioms apply. I hope you see my confusion here. Edited June 27, 2015 by ajb
John Cuthber Posted June 27, 2015 Posted June 27, 2015 John If I hold 5 apples and divide them by zero I still hold 5 apples What would you do to divide 5 apples by zero? If I wanted to divide 10 apples between 2 people I would give each person an aple, in urn, until I ran out of apples- they would have 5 each and I'd have none. If I divided them between zero people I would give away zero apples util I ran out. But I'd never run out would I ? So I could never do it. So I can't divide 5 apples by zero. Why don't you face up to that?
conway Posted June 27, 2015 Author Posted June 27, 2015 (edited) John "If I divided them between zero plp I would give away zero apples until I ran out. But I'd never run out would I?" EXACTLY...so you still have five apples, why don't you face up to that? Ajb Yes the distributive is kept, the additive inverse is kept. That is... A*A-A*A=0 A(Z1) * A(Z2) = A z1 For A = A z2 For A = A (Az1 * Az2)-(Az1 * Az2) = 0 Edited June 27, 2015 by conway -1
John Cuthber Posted June 27, 2015 Posted June 27, 2015 John "If I divided them between zero plp I would give away zero apples until I ran out. But I'd never run out would I?" EXACTLY...so you still have five apples, why don't you face up to that? When would I have five apples? It can't be after I have give them away, but I haven't done the division until after I have given them away. So there's nothing for me to face up to is there? That's the point; the division is impossible.
conway Posted June 27, 2015 Author Posted June 27, 2015 (edited) John. post #31 you state... "If I divided them(apples), between zero plp, I would give away 0 apples until I ran out" - If I have X apples and give them away 0 times, then clearly I still have X apples. This is not the same as If I have 0 apples and give them away X times, then clearly I have 0 apples. 0 * A = 0 = 0z1 * Az2 = 0 = Az2 * 0z1 = 0 A * 0 = A = Az1 * 0z2 = A = 0z2 * Az1 = A Edited June 27, 2015 by conway 1
John Cuthber Posted June 27, 2015 Posted June 27, 2015 You didn't answer the question. What would you do to divide 5 apples by zero? If you have 15 apples and give 0 of them away to 0 people then you have done nothing; you certainly have not divided anything by anything. If you wanted to divide those ten apples among 5 people (ie calculate 15/5 you would give an apple to each person, then go back and give each person a secod appl, then go back and give them a third apple each. At that point you have run out of apples- that's how you know that you have finished doing the division. If you don't run out of apples, you don't stop. If you don't stop then you have not finished doing the division. So, as I said, how do you divide 5 apples among zero people? Here's a hint; you can't. 4
Unity+ Posted June 27, 2015 Posted June 27, 2015 I wonder how many times this topic will keep popping up, considering how many times it has been brought up on many other forums. Can't people just accept you can't divide by 0?
conway Posted June 27, 2015 Author Posted June 27, 2015 You can, by not doing anything at all. If I have five apples, and I don't do anything, then I have done the equivalent of dividing and multiplying by zero. I have tried to answer your question. 1
Greg H. Posted June 27, 2015 Posted June 27, 2015 The problem is not that the question yields multiple answers. The question n/0 yields literally an infinite number of answers. There are so many answers that having the answer does not, in any way, help you better understand the problem. Here's the example I give people when they ask me this question. Take a pie. Now, divide it into 0 parts without destroying the pie. There may be some systems of mathematics where division by 0 is defined differently than it is in everyday algebra and arithmetic. But by and large, the answer is undefined (or indeterminate) You can, by not doing anything at all. If I have five apples, and I don't do anything, then I have done the equivalent of dividing and multiplying by zero. I have tried to answer your question. Actually you have done the equivalent of multiplying and dividing by 1, not 0. I wonder how many times this topic will keep popping up, considering how many times it has been brought up on many other forums. Can't people just accept you can't divide by 0? They do once they come to grips with the fact that 0 isn't really a value. It's a lack of value. I had that epiphany when I starting learning binary and came to realize that the 0s in binary numbers are just placeholders for numbers that aren't there.
conway Posted June 28, 2015 Author Posted June 28, 2015 (edited) Greg H. It is not that 0 has no value. It is that it is value that is undefined. As a fact no value does not exist. Value is everywhere. Also my statement was equivalent to multiplying by one. I agree. I have proposed an axiom to follow all current field axioms. Post #23 Additionally 0 in binary is not the same as 0 in mathematics. Edited June 28, 2015 by conway
John Cuthber Posted June 28, 2015 Posted June 28, 2015 It is not that 0 has no value. It is that it is value that is undefined. Additionally 0 in binary is not the same as 0 in mathematics. Nonsense. Zero is perfectly well defined and it's also physically meaningful- it is the number of cows in my bedroom (among lots of other things). Since binary is part of mathematics what you have said is that the zero on maths isn't the same as the zero in maths- that's obviously nonsense too. if you try to construct a system of maths where both multiplication by zero and multiplication by 1 give the same answer, then you have constructed a system with a built in contradiction (since it implies that 1 is simultaneously equal to zero, and not equal to zero). That's not going to be any use. Can you show that you are not a victim of this phenomenon? https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect
Strange Posted June 28, 2015 Posted June 28, 2015 Additionally 0 in binary is not the same as 0 in mathematics. What is the difference between "0 in binary" and "0 in mathematics"? 0 in any base is 0. Why would binary zero be different from decimal zero?
ajb Posted June 28, 2015 Posted June 28, 2015 If I have five apples, and I don't do anything, then I have done the equivalent of dividing and multiplying by zero. You mean multiplying by one. Other words you want 1 = 0/0, which is where all the troubles start. 2
conway Posted June 28, 2015 Author Posted June 28, 2015 (edited) It is only that they are "philosophically equivalent". The only real definition for division is the inverse of multiplication. 0 in binary is a bit of information. That is 0 in binary is "on,or off" "open, closed" "yes, no", where as in mathematics it is the representation of a value that is undefined. Or "nothing" as john so insists. Again it is a physical FACT, that nothing does not exist. That means "no values" do not exist. While I may have zero apples, I do not have nothing, nor will I ever. Even if all I hold is an empty dimensions, that is still a something AJB 0/0=0 and always will. If z1 and z2 for zero must both be used, then the answer will always be zero. It is only that 0 has properties of 1, and 0, that is why there is the confusion on it's "similarity" to 1. John not always in multiplication by zero and by 1 equivalent. I gave an axiom. Thus there is not inconsistency. Insulting me is not necessary. I will be the first to tell you what it is I do not know. Did I not start this thread off by asking for help, asking a question? It is only you JOHN that has claimed to have all the correct answers so I wonder if then it is you that suffers from the dunning kruger affect? Edited June 28, 2015 by conway 1
Strange Posted June 28, 2015 Posted June 28, 2015 0 in binary is a bit of information. That is 0 in binary is "on,or off" "open, closed" "yes, no", That is not true. Where did you get that idea? 0 in binary is exactly the same as 0 in octal, decimal or any other base. where as in mathematics it is the representation of a value that is undefined. That is not true either. 0 is very well defined. Again it is a physical FACT, that nothing does not exist. That means "no values" do not exist. While I may have zero apples, I do not have nothing, nor will I ever. I don't think I can put into words what I think of that argument. Irrational is probably the closest I can get. If the number of apples you have is zero (in binary or hexadecimal) then that means you have no apples. That's all. It doesn't say anything about the number of oranges, dubloons or zebras you have.
conway Posted June 28, 2015 Author Posted June 28, 2015 (edited) Given the validity of all axioms found in the link on #17 Given the validity of the axiom I offered.(allowing in / z1 is always first, z2 is always 2). 0 = (Z1=0,Z2=1) A= (Z1=A,Z2=A) 0/0 = (z1 / z2 ) = 0 0/A = (z1/z2) = 0 A/0 = (z1/z2) = A 0*0 = (z1 * z2) = 0 0*A = (z1 * z2) = 0 0*A = (z2 * z1) = A A*0 = (z1 * z2) = A A*0 = (z2 * z1) = 0 Strange I can concede that my understanding of binary is completely wrong. I don't see that it makes a difference in any case. "If you have zero apples in (binary or hexadecimal), then it means you have no apples." I agree it says nothing of oranges or zebras....but if you don't have apples..... what do you have. You do not have "NOTHING". Therefore your value while it is zero, is not "nothing". Edited June 28, 2015 by conway 1
John Cuthber Posted June 28, 2015 Posted June 28, 2015 0/0=0 and always will. It is only you JOHN that has claimed to have all the correct answers Do you realise that the second part of that contradicts the first part? Ditto "Additionally 0 in binary is not the same as 0 in mathematics." followed by "I can concede that my understanding of binary is completely wrong. I don't see that it makes a difference in any case." So, once again Can you show that you are not a victim of this phenomenon? https://en.wikipedia...
conway Posted June 28, 2015 Author Posted June 28, 2015 (edited) John Please lets drop the rude posting here? I will listen to you. But you need to stop claiming I have dunning kruger issues. The very fact that I have admitted my ability to be wrong, proves this is not the case. You however have yet to admit that ability. Edited June 28, 2015 by conway 1
Bignose Posted June 28, 2015 Posted June 28, 2015 (edited) 0 = (Z1=0,Z2=1) A= (Z1=A,Z2=A) All you're doing here is making '0' a 2-D vector object of some sort. And then making your own rules about that 2-D vector space. And not using very good vector notation which is why a lot of this isn't very clear. This doesn't answer anything about a 1-D object like the number line wherein division by 0 is undefined and 0/0 is indeterminate. Not to mention that 2-D vector spaces already have a zero element 0 = (0, 0) that follows most of the exact same rules that the 1-D 0 follows. Edited June 28, 2015 by Bignose
Strange Posted June 28, 2015 Posted June 28, 2015 I can concede that my understanding of binary is completely wrong. I don't see that it makes a difference in any case. So why bring it up? "If you have zero apples in (binary or hexadecimal), then it means you have no apples." I agree it says nothing of oranges or zebras....but if you don't have apples..... what do you have. You do not have "NOTHING". Therefore your value while it is zero, is not "nothing". This is what is known as a "straw man" fallacy. No one says that zero apples means nothing. But, of course, because mathematics doesn't need to have any relation to the real world, it is quite possible to use 0 to represent nothing.
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