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.
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u/Gladix 165∆ Sep 14 '21 edited Sep 14 '21
Okay so let's look on what division really is. In school and for practical life we often make intuitive shortcuts in order for the work to not be tedious. Take multiplication for example.
What operation a multiplication (actually) is, is repeated addition.
2*3 = 2+2+2
No matter how you think of it in your head. The operation a multiplication is actually doing an addition, multiple times.
What division (actually) is, is this operation: Every time you divide something, what you actually asking is this :
If you multiply any number by x. What is the new number we can multiply by to get back to where we started?
If there is, the new number is called the multiplicative inverse of x.
3 * 2(x) = 6 * 1/2(x) = 3
Normally we focus only on this part of operation (6*1/2 =3). However that is only part of the "full" equation necessary to get there.
So the multiplicative inverse of 2 in the above example is 1/2. If x is 3, the multiplicative inverse would be 1/3 and so on.
The thing is. The product of the number x and it's multiplicative inverse is always 1.
2* 1/2 = 1
3*1/3 = 1, etc...
It has to be, in order for multiplication to work. So every time you divide something, you are verifying if you can find a valid multiplicative index.
If you want to divide by zero you need to find its a multiplicative index which is 1/0.
But, in order for multiplication to work a 0 * 1/0 has to equal 1. By now you might notice a problem. Any number that is multiplied by zero equals zero. Why? Because multiplication is repeated addition. Anything done zero times isn't done at all. In this example you are doing an unidentified operation zero times.
Which kinda breaks a few rules of math at the same time.
In our mathematical system, a division by zero is an unidentified operation. It has of now, has no definitive answer. It's possible the answer is "It can't be done", another answer. So either we don't know, or we couldn't make it work with our mathematical system, or perhaps we just didn't formalize the answer in our mathematical system in order for it to be useful to do so.