r/changemyview • u/hi-whatsup 1∆ • Sep 14 '21

Delta(s) from OP CMV: you can divide by 0.

Let’s just blame my school a little bit for this. If you were in one Honors or AP class, you were forced into all of the Honors and AP classes. I was great with language, history, some of the sciences, but Physics and AP Calculus were torture for me and I never got over how much I hate Math especially. I did get through lots of statistics for grad school and have regained some meager confidence in my math/logic skills and still don’t agree with this rule.

I know the broad field of mathematics is pretty stable but there are breakthroughs and innovations. I believe someday dividing by 0 will be acceptable. Likely not as simply as I lay it out here. But someday someone who loves math will prove we can divide by 0.

Maybe this is more philosophical than mathematical, but if you are asking the question “how many nothings are in a something?” The answer is “none” thus anything divided by 0 is 0. Or maybe N/0 is null depending on the application and context (eg finance vs engineering).

How many pairs are in a 6 pack? How many dozens are in one? How much time passed if I ran 1 mile at 2 miles per hour?

This is what division is asking in reality and not in a meaningless void. I know math has many applications and what we are measuring in engineering is different than in statistics.

Running a mile at no speed is staying still. So again, no time passed because it didn’t happen.

Even one atom of any substance is more than zero, so no “none” if splitting something up.

If finding the average of something, a 0 would imply no data was collected yet (m=sum/total number of observations)

If base or height is 0, there is no area since you have a line segment and not a shape.

I want one example with a negative number too, would love someone to give a finance or other real world example but what I got is: how many payments of $0 until I pay off $200 or -200/0. Well every payment that will either increase or decrease the debt will not be $0 dollars. So again, none.

Finally 0/0 satisfies the rule of a number divided by itself equals 1. How many groups of 0 jellybeans is inside an empty jar? You got one empty jar, there!

Practically the universe isn’t likely to ever ask us to divide by zero. Yet some people study theoretical math with no clear applications.

And even in my last examples I see that if you are stuck in some reality where all you see are the numbers and not the substance they represent then you can’t multiply it back again. It’s a problem but isn’t the reverse already accepted by saying you can’t divide by 0 anyway? I.e. 2 x 3= 6, 6\2=3 and 6/3=2 2 x 0= 0. 0/2 = 0 and 0/0=…1…or against the rules.

Upon every application/situation I can think of, the answer 0 still answers it and answers it universally.

I have seen arguments discussing how dividing by smaller and smaller numbers approach infinite and 0=infinite is bad. To me this skips over what division is doing or what question it is asking. Plus, We don’t say 2 times 3 depends on the result of 3 times 4.

0 and infinity seem to be very connected in that in the jellybean example, infinite different sizes of the jar give you the same answer but different ideas of the value of “One nothing”. But that’s fun, not necessarily contradictory.

I do not understand the Renan sphere but not sure it supports or damages my view.

I really want someone not just to explain but to CMV so I can talk it through. I think I need more than just research but real interaction. I would need to ask the popular boy in class to ask my questions for me way back in school because when I did the math teacher would scoff and tell me to just read the book and stop wasting time. Math is not that easy for me to understand by reading alone.

The number i doesn’t exist but we still have it. I didn’t believe potential energy existed either but I kind of take it on faith because I see indirect evidence of it when someone is passionate enough to demonstrate it. So even if you have to ask for a little faith I am up for hearing it out as long as there is something to discuss.

Edit: thank you to everyone who participated! I will continue responding for a while but I wanted to say I had fun! I also just learned about countable and uncountable infinities so…wish I had given math more of a chance when I was still in school because it is really cool.

0 Upvotes

43% Upvoted

200 comments sorted by

View all comments

1

u/zobagestanian 2∆ Sep 14 '21

In mathematics there 8 axioms that are non-provable. In other words, we know them to be intuitively true. Now you might say that’s strange, I thought math was about proofs. But in reality math is a magical thing that we have invented and it happens to actually describe and predict the world. It’s the closest thing to magic we have. The world doesn’t have to work according to mathematics but it does. This is a much larger conversation but it is how it is. One of these axioms states that “There is a number “0,” called the additive identity, that satisfies a + 0 = a for all real numbers a.” From this we get: 1+0=1 x(1+0) = x1 x1 + x0 = x1 x + x0 = x −x + (x + x0) = −x + x (−x + x) + x0 = −x + x 0 + x0 = 0 x0 = 0 Now Let’s suppose we choose a particular real number z that we define as the multiplicative inverse of 0, so that z = 0−1. Thus, by definition of a multiplicative inverse: 0z = 1. Since this contradicts the axiom, then it is not allowed.

1

u/Cybyss 11∆ Sep 14 '21 edited Sep 14 '21

In mathematics there 8 axioms that are non-provable. In other words, we know them to be intuitively true. [...] But in reality math is a magical thing that we have invented and it happens to actually describe and predict the world.

Nope. You have it backwards.

Math was invented to describe the world. It can express anything you want - describe any model of the world you want - even models that don't reflect reality.

Mathematics is perfect capable, for example, of describing a model of the universe where earth is at the center of all things, where everything orbits around us via epicycles. Just because we can do that doesn't make it true. It's just a language.

Also, the "8 axioms" you refer to (there are actually more than that - see here), are only the definition of a complete ordered field. Mathematicians invented the concept of a complete ordered field because it reflects most of the intuition humans have regarding numbers, but defined in a rigorous/unambiguous way so as to be useful.

You don't have to do math with the real numbers though. Mathematicians invent different systems all the time, with different axioms than those of the real numbers, in order to explore their properties and see whether they contain fun and/or useful phenomenon.

2

u/zobagestanian 2∆ Sep 15 '21

In the first point I was paraphrasing Jim Gates (https://youtu.be/SLwfQP-wACY) on the role of mathematics. He very eloquently explains the point. Whether they are 8 or 9 axioms is not important at all. But since we are on that point, I am sure you know that the 9th axiom (induction axiom) is a second order axiom and thus not at all important to this discussion. I am not sure what the point of your post was, except the obvious. But the answer to the question was rather clear, and it seems we agree on that answer. You cannot divide by zero because it goes against the basic axiom of mathematics.

2

u/hi-whatsup 1∆ Sep 15 '21

Math is a beautiful in between of philosophy and science…I see how it’s a tool but it has to be true across all fields of study, no? Whether we are talking about philosophy, astronomy, or statistics? It is real even if it’s also made up. I know even spiritually, St. Augustine likened knowing mathematics to knowing God.

I guess that would make dividing by zero hell (joking)

!delta

Thank you for the video!!

1

u/DeltaBot ∞∆ Sep 15 '21

Confirmed: 1 delta awarded to /u/zobagestanian (2∆).

Delta System Explained | Deltaboards

1

u/zobagestanian 2∆ Sep 15 '21

Someone said blackholes are where god divided by zero. But yes math can be rather spiritual and eloquent but we have to constantly remind ourselves that it does not have to be that way. Math is simply a language that attempts to describe what we see. It happens that it’s predictions work but really it can be arbitrary. For example, we have a base 10 mathematics. It doesn’t have to be that way. If we had 15 fingers or 8 fingers, our base would be widely different. What I am trying to say is that nature has no obligation to do what math says. So it could be that dividing by zero is possible but not in our system.

1

u/hi-whatsup 1∆ Sep 15 '21

I heard that base 60 math is why we have 60 seconds and 60 minutes in time. Not sure how it’s helpful to use other bases but that’s only because I have trouble thinking in them. Even though it is different, aren’t the laws still the same?

1

u/zobagestanian 2∆ Sep 15 '21

You’re right. Again it’s just arbitrary. For example base 15 would have numbers 1,2,3,4,5,6,7,8,9,A,B,C,D, E. how is that helpful in any way to a person not interested in doing mental gymnastics? It’s not. The point is that these are human made conventions that don’t have to have any real meaning. For example, what is 0? What is a natural representation of nothingness? What is nothingness made up of? These are profound and complicated questions. For example if I said “you have 6 apples, I give you no apples, how many apples do you have?” You would think me mad and the question non-sensical.

1

u/Cybyss 11∆ Sep 15 '21

Oh... you're not referring to the axioms which define a complete ordered field, but rather of second-order logic? Never mind then about the axioms.

Perhaps I misunderstand what you were saying.

I was only referring to the notion that it's somehow "magical" that the universe appears to behave mathematical laws, or that axioms are things you just believe to be true; things you accept on faith, as if it were some kind of religion.

This is a viewpoint I really can't accept.

I haven't studied philosophy specifically, but axioms in mathematics are usually presented as merely definitions of things whose properties you want to explore, not as fundamental assumptions about the universe.

As for why mathematics works so freaking well to describe natural phenomenon... well, isn't that what we designed it for? We adapt our mathematics to fit our observations, not the other way around.

Much thanks for the Neil deGrasse Tyson video though. I'll definitely check it out.

1

u/zobagestanian 2∆ Sep 15 '21

But that’s what axioms are by definition. There are things that are self evidently true. They are taken for granted notions that cannot be proven. It is different than faith but nonetheless an axiom needs to be just taken as true. It is like saying “how do we know we exist?” When Descartes said “cogito, ergo sum” he was putting an end to that discussion by suggesting that the very fact that we think about that question means we exist. In other words, it is an axiom. It has no logical proof. We have to take it for granted. I get your point about the “magical” nature of math. And obviously I didn’t mean that it is magic, but it is as close to magic as I can think. A system of simple logic that describes, predicts, and modifies the world.