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-   -   A thought on Division in Mathematics (https://www.mersenneforum.org/showthread.php?t=25640)

BillyB 2020-06-17 21:00

A thought on Division in Mathematics
 
I have developed a new way to think about division that attempts to explore a lot of different avenues in helping us understand the world around us. All I am looking for are your thoughts and feedback. If we developed a discussion about this that would be even better. 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:

As opposed to just saying 1/2=.5, my theory is read as:

1)0 = (1)(1.0 or 100%) or
1)1 = (2)(0.5 or 1/2 or 50%)

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.

There is obviously a lot more to this but again I am keeping it short. I would love to explain further if there is any interest in this but only time will tell. I look forward to your thoughts and opinions. Thank you!

Uncwilly 2020-06-17 21:13

There is nothing new here. I was taught the same basic thing in elementary school.

BillyB 2020-06-17 21:44

Wow. I presented this to a couple of my mechanical engineering professors and they had great things to say about it. Was it taught to you as a formal theory or just an idea? Were there any new operation symbols that were used to present the material or was it just a concept with no proof? What applications were found to be useful with it? Thank you for your gracious feedback.

Uncwilly 2020-06-17 21:48

It is, as far as I can see basically the same as teaching division using a pizza.
[YOUTUBE]87RY-sM5Pa0[/YOUTUBE]

BillyB 2020-06-17 21:50

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.

jnml 2020-06-18 08:41

[QUOTE=BillyB;548314]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]

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?

Nick 2020-06-18 09:24

[QUOTE=BillyB;548302]I look forward to your thoughts and opinions.[/QUOTE]
For ordinary division, your way of looking at it makes a lot of things harder.
Simple rules for multiplying fractions, for example, become more complicated.

There are other areas of mathematics in which we "count the cuts not the parts", however.
The length of a finite chain of sets, each containing all the previous ones is defined that way. For example
\[ A\subset B\subset C\]
is a chain of length 2. In algebra at university level, this idea is then used to define concepts such as the Krull dimension of a commutative ring,
which is important in Algebraic Geometry.

BillyB 2020-06-18 15:32

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)
1)1=(2)(.5)
1)2=(3)(.33333)
1)3=(4)(.25)
No extra steps are required and when the results are multiplied together they return you where you started whether that be 1)1 or 2)1 or 3)1 etc. Again, I believe this changes the way we think and the choices that we make on a day to day basis given that math is the universal language and we all live by it. The main problem is that it is a paradox or contradictory by design leaving all of us no choice but to be walking contradictions ourselves (me included).

BillyB 2020-06-18 15:35

My goal is to make the world a better place and this starts with me trying to become a better person myself. It takes humility and honesty and self reflection to evolve in a positive manner. I wish that we can all do so to create a more peaceful existence here on planet Earth.

Uncwilly 2020-06-18 15:54

How does this help with 23 / 57 or 22 / 7?
Or 101 / 0.037? Or 123456789 / 0.0000987?

Inventing new notation for something that has a well established notation system is a way for people to not take you seriously.

BillyB 2020-06-18 22:31

I couldn’t agree more so let me be clear. This isn’t designed to replace our current division. It is included in this so I apologize for not being clear enough. It is simply another way of thinking about it.


1)1=(2)(1/2) or (2)(.5) Our division is still in place. I’m just expanding it. When 1 thing is actually cut or divided 1 time you would be left with 2 pieces half their original size. Then it becomes its own piece so if more cuts were made you could start the process all over knowing the original physical dimensions of the part or piece.

It could also be written as: 1)1=(.5) + (.5) (2 things that are .5 of their original size).

The current system to me is a useful way of equating a fraction to a decimal. Nothing more is really happening in my humble opinion. The above equation is a purely ideal case with no remainder (like no sawdust left from using a saw to cut a board). The split could be a 70/30. This leads me to wanting to get into how we make decisions. Say you have a choice to make and you are 70% sure about something and 30% unsure. In that case you’ll most likely choose the 70% option.

Now if want to cut anything less than a full cut it gets complicated but I’m happy to explore that avenue as well but it needs to be developed. I’m happy to have you taking part in this discussion.


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