mersenneforum.org A thought on Division in Mathematics
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2020-06-23, 16:07   #45
BillyB

Jun 2020

29 Posts

Quote:
 Originally Posted by Uncwilly I don't think "great things" fits with "contradicts". If you weren't sure what he meant, you should have have asked. Maybe he was trying to tell you to go find out why your idea fails. Maybe your memories have altered the facts since you left school years ago. If it contradicts everything in the math department, then either your idea is flawed, or all of known math is wrong.
Some feedback I received was in person, on the phone or via email. I still have the emails.

2020-06-23, 16:09   #46
BillyB

Jun 2020

29 Posts

Quote:
 Originally Posted by storm5510 Off-topic, somewhat. Seeing all the fractions in the pizza video reminded me of my father. He worked over 25 years in a road construction machine factory. He could look at a bolt head or a nut and say what size it was. He would get 8th's and 16th's right every time. He was also a part-time carpenter. He could glance at a tape-measure and do the same thing. He struggled with millimeters when it became common much later in his life.
In my opinion this is right on topic. Imagine living your entire life learning and perfecting something one way and then having a new system or way of doing something introduced. It would be difficult for most people to just accept it as is and understand it right away. Thank you for your post.

 2020-06-23, 16:55 #47 CRGreathouse     Aug 2006 10110111001102 Posts It's hard for me to believe we're five pages in and you still haven't defined your operation. You have a function -- not division, but your new take on it -- which takes two arguments and returns a third. Let's call it BillyB(x, y) = z. For which pairs of x and y is BillyB(x, y) defined? When BillyB(x, y) is defined, how can BillyB(x, y) = z be computed? Are there some pairs x and y for which BillyB(x, y) = x/y or BillyB(x, y+1) = x/y?
2020-06-23, 17:37   #48
paulunderwood

Sep 2002
Database er0rr

22·72·17 Posts

Quote:
 Originally Posted by retina 1/0 is how many times can we cut things of size 0 from a thing of size 1.
is that bigger than $$\aleph_{1000}$$?

2020-06-23, 18:25   #49
BillyB

Jun 2020

29 Posts

Quote:
 Originally Posted by CRGreathouse It's hard for me to believe we're five pages in and you still haven't defined your operation. You have a function -- not division, but your new take on it -- which takes two arguments and returns a third. Let's call it BillyB(x, y) = z. For which pairs of x and y is BillyB(x, y) defined? When BillyB(x, y) is defined, how can BillyB(x, y) = z be computed? Are there some pairs x and y for which BillyB(x, y) = x/y or BillyB(x, y+1) = x/y?
You are on the right track! I will reply more later tonight as I don’t have the time this minute to go further into detail. Thank you for your post!

2020-06-23, 18:26   #50
BillyB

Jun 2020

29 Posts

Quote:
 Originally Posted by CRGreathouse It's hard for me to believe we're five pages in and you still haven't defined your operation. You have a function -- not division, but your new take on it -- which takes two arguments and returns a third. Let's call it BillyB(x, y) = z. For which pairs of x and y is BillyB(x, y) defined? When BillyB(x, y) is defined, how can BillyB(x, y) = z be computed? Are there some pairs x and y for which BillyB(x, y) = x/y or BillyB(x, y+1) = x/y?
It is a function but I was told by a math professor that I have the utmost respect for to call it a new thought on division so I stuck with that until I realized the formula that it created. You can use it to graph coordinates as well.

2020-06-23, 18:26   #51
Uncwilly
6809 > 6502

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

172×29 Posts

Quote:
 Originally Posted by Uncwilly 45
I rechecked and I think 65 is a closer value.

Some dude that likely lives in rural 'merica at the end of a gravel road thinks he found something new with regards to basic math. It has been known for ~1500 years that division by zero is absurd.

2020-06-23, 19:30   #52
BillyB

Jun 2020

29 Posts

Quote:
 Originally Posted by Uncwilly I rechecked and I think 65 is a closer value. Some dude that likely lives in rural 'merica at the end of a gravel road thinks he found something new with regards to basic math. It has been known for ~1500 years that division by zero is absurd.
Why are you so offended by this? And no, you have me all wrong. How would anything new be created if it weren’t for new ideas?

2020-06-23, 19:47   #53
xilman
Bamboozled!

May 2003
Down not across

10,163 Posts

Quote:
 Originally Posted by BillyB Why are you so offended by this? And no, you have me all wrong. How would anything new be created if it weren’t for new ideas?
1) I am not in the least offended.
2) I agree whole-heartedly.

That said, please define the function which has been called "BillyB".

Here is a first take, based on what I have read so far. I am very far from infallible so my definition may be completely wrong.

Let x and y be real numbers.

BillyB(x, y) = x/y for all x, y where x and y are both non-zero.
BillyB(x,0) = 1 for all x not equal to zero.

At the moment I have no idea of the value of the only remaining case, viz BillyB(0,0).

Please enlighten me. This is especially true for the third case, "0/0".

Last fiddled with by xilman on 2020-06-23 at 19:54 Reason: Remove otiose comma

2020-06-23, 20:48   #54
bsquared

"Ben"
Feb 2007

3,271 Posts

Quote:
 Originally Posted by xilman Here is a first take, based on what I have read so far. I am very far from infallible so my definition may be completely wrong. Let x and y be real numbers. BillyB(x, y) = x/y for all x, y where x and y are both non-zero. BillyB(x,0) = 1 for all x not equal to zero.
I agree with the first but my take on his "explanation" so far is that BillyB(x,0) = x. i.e., a thing of size x cut zero times remains size x. So BillyB(0,0) = 0 by that definition.

but that assumes some definitions... namely that x is the quantity or size of a cuttable object and y is the number of times to cut it into equal pieces. Then BillyB(x,y) = x / (y+1). Physically you can only cut something zero or more times so the domain of the function is >= 0. So, by that definition, there is no dividing by zero possible, by the everyday/ordinary definition of "divide". BillyB is not a division operation but some kind of splitting operation.

[edit-edit]
I suppose that must mean that x, y are in $\script{N}^0$. The guess at a definition doesn't work otherwise....

Last fiddled with by bsquared on 2020-06-23 at 21:06

2020-06-23, 23:08   #55
BillyB

Jun 2020

2910 Posts

Quote:
 Originally Posted by bsquared I agree with the first but my take on his "explanation" so far is that BillyB(x,0) = x. i.e., a thing of size x cut zero times remains size x. So BillyB(0,0) = 0 by that definition.  but that assumes some definitions... namely that x is the quantity or size of a cuttable object and y is the number of times to cut it into equal pieces. Then BillyB(x,y) = x / (y+1). Physically you can only cut something zero or more times so the domain of the function is >= 0. So, by that definition, there is no dividing by zero possible, by the everyday/ordinary definition of "divide". BillyB is not a division operation but some kind of splitting operation. [edit-edit] I suppose that must mean that x, y are in $\script{N}^0$. The guess at a definition doesn't work otherwise....
Excellent interpretation!

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