mersenneforum.org A thought on Division in Mathematics
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2020-06-23, 12:09   #12
BillyB

Jun 2020

29 Posts

Quote:
 Originally Posted by jnml Pardon my ignorance, but I have no idea what, new or not, theory you're talking about. I see here only a (over)simplified and vague/insufficient definition of division. But the division by zero gets my attention. So, can you please share some example of dividing by zero with the results?
Have you had a chance to read my further posts describing 1/0??

2020-06-23, 12:18   #13
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

5,741 Posts

Quote:
 Originally Posted by BillyB Currently we can’t divide by zero. This is a paradox. It just doesn’t make sense and that is why is it left as undefined. No better way of explaining division has ever been formally developed. When you look at and think about 1/0 there are two possibilities. It should be 1 but at the same time it should be 0. This occurs due to certain rules that have been laid out long before any of us existed (i.e. multiplying both sides by the denominator). If we were able to adopt a new way of thinking about division, say for example my theory, it is fully defined and provides a solution when 0 is used. See again: 1)0=(1)(1)
Your example isn't division by zero. It is division by one. Using your analogy:

You cut something zero times, means you divide by one.
You cut something one time, means you divide by two.
etc.

So to divide by zero, you need to cut something negative one times. How can you do that?

2020-06-23, 12:20   #14
jnml

Feb 2012
Prague, Czech Republ

22·41 Posts

Quote:
 Originally Posted by BillyB Have you had a chance to read my further posts describing 1/0??
Yes I did. As your notation was not defined at all, I can only guess if I have inferred it right.

Let's test that: Is post #1 saying that 1 divided by zero is equal to one?

2020-06-23, 13:39   #15
BillyB

Jun 2020

29 Posts

Quote:
 Originally Posted by jnml Yes I did. As your notation was not defined at all, I can only guess if I have inferred it right. Let's test that: Is post #1 saying that 1 divided by zero is equal to one?
No. Division is a different concept from my theory. My theory includes our current division but 1 divided by 0 is omitted on the right hand side of the equation. The left side of the equation is the actual or physical cut. I can’t call it division because division already exists and is well established. The division that is in included starts at 1/1 and the denominator gets higher as the size of the pieces from the “cut” decreases. 1 cut 1 time equals 2 pieces half their original size. Currently we say 1 divided by 2 equals one half or .5 or 50%. But if we are dividing something shouldn’t we be left with two half’s regardless of their size? It seems like our current division is a very useful tool in equating a fraction to a decimal. Nothing more seems to be happening in my humble opinion.

2020-06-23, 13:44   #16
BillyB

Jun 2020

29 Posts

Quote:
 Originally Posted by retina Your example isn't division by zero. It is division by one. Using your analogy: You cut something zero times, means you divide by one. You cut something one time, means you divide by two. etc. So to divide by zero, you need to cut something negative one times. How can you do that?
We must keep division and this cut theory separate as our current division is well defined and established. Having said that if I have one thing and I don’t cut it I still have that one thing at 100% of its original size. If I cut that one thing one time then I could ideally have 2 things half of their original size. The division is on the right hand side of my equation and starts at 1/1, and then 1/2, 1/3 etc. the zero can be omitted on the left hand side if it isn’t necessary.

Last fiddled with by BillyB on 2020-06-23 at 13:49

2020-06-23, 13:49   #17
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

5,741 Posts

Quote:
 Originally Posted by BillyB Having said that if I have one thing and I don’t cut it I still have that one thing at 100% of its original size.
That is just division by 1.

How do you represent division by zero? It seems like you just want to ignore it and pretend it doesn't exist.

2020-06-23, 13:53   #18
jnml

Feb 2012
Prague, Czech Republ

22·41 Posts

Quote:
 Originally Posted by BillyB No.
This is what happens when you invent a notation but you keep its meaning to yourself.

Please explain and define the notation you're using. Don't let people guess the meaning.

Make an example, and comment all the parts used in the notation. Maybe using the
standard known notation would just work?

Also, why are you talking about a "theory"? Where's a/the "theory"? What does the "theory"
explain and/or predicts? I'd not call deriving some facts a "theory".

But who knows, when you cannot properly explain your thoughts to others. So start right

2020-06-23, 13:53   #19
BillyB

Jun 2020

2910 Posts

Quote:
 Originally Posted by retina Your example isn't division by zero. It is division by one. Using your analogy: You cut something zero times, means you divide by one. You cut something one time, means you divide by two. etc. So to divide by zero, you need to cut something negative one times. How can you do that?
In one of my previous posts I state that division by zero is a paradox. It cannot be solved logically or rationally. This remains true in my theory but it never presents itself due to the nature of my explanation. It seems logical and rational to me that if I have something and I don’t cut it then I’ll still have the one thing. But division is different. In my opinion it’s a useful way of equating a fraction to a decimal. 1/0 is a paradox because it should or could be 1 and/or 0 at the same time.

2020-06-23, 13:58   #20
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

166D16 Posts

Quote:
 Originally Posted by BillyB In one of my previous posts I state that division by zero is a paradox. It cannot be solved logically or rationally. This remains true in my theory but it never presents itself due to the nature of my explanation. It seems logical and rational to me that if I have something and I don’t cut it then I’ll still have the one thing. But division is different. In my opinion it’s a useful way of equating a fraction to a decimal. 1/0 is a paradox because it should or could be 1 and/or 0 at the same time.
I'm not asking for a result. I'm asking for how you represent it. Using normal division I can write x/0. How would you write it?

2020-06-23, 13:59   #21
BillyB

Jun 2020

358 Posts

Quote:
 Originally Posted by jnml This is what happens when you invent a notation but you keep its meaning to yourself. Please explain and define the notation you're using. Don't let people guess the meaning. For example , all your samples start with '1)'. Why? What it means? Make an example, and comment all the parts used in the notation. Maybe using the standard known notation would just work? Also, why are you talking about a "theory"? Where's a/the "theory"? What does the "theory" explain and/or predicts? I'd not call deriving some facts a "theory". But who knows, when you cannot properly explain your thoughts to others. So start right there, please.
Thank you for your feedback. I thought I explained it clearly but I understand it thoroughly so I apologize if it seems as though I left something out. Also, I posted here to drive a discussion which takes time to cover all the details. It is hard to just throw everything out and expect everyone to understand where I am coming from. As far as my notation I picked the best thing I could. It can be a completely new symbol and different from what I have chosen but the point was to reach out and get opinions on it. If we put a team together to truly work this out decisions would be made as a group and not just by me. I believe it’s a theory that involves a lot of different areas that need to be talked about in detail which again takes time. Understanding the math I thought was the right way to go at first.

Last fiddled with by BillyB on 2020-06-23 at 13:59

2020-06-23, 14:03   #22
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

89·97 Posts

Quote:
 Originally Posted by BillyB In one of my previous posts I state that division by zero is a paradox. It cannot be solved logically or rationally. This remains true in my theory but it never presents itself due to the nature of my explanation.
Quote:
 Originally Posted by BillyB I believe the implications of this are huge. I will keep this short for now for the sake of all of our time but the basic idea is as follows: ... 1 thing cut 0 times equals 1 thing at 100% of its original size. The second example is read similarly but when 1 thing is cut 1 time it equates to 2 things at 50% of their original size.
Quote:
 Originally Posted by BillyB Except when it comes to 1/0. Our current division is 99.999999999% accurate but why would we accept anything but perfection? Perhaps a better solution has never been created. I am not saying my theory is perfect but that is why I am here, to develop it and develop an open discussion around it. My theory allows the use of 0 or it can be completely removed.
Quote:
 Originally Posted by BillyB If we were able to adopt a new way of thinking about division, say for example my theory, it is fully defined and provides a solution when 0 is used.
You now say that you haven't fixed it. Before you said you did. Pick one stance or admit you are/were wrong.

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