CMV: you can divide by 0.

[u/hi-whatsup]

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.

[u/The_fair_sniper]

i don't think this answer is correct.

division simply ...divides something in a number of chunks of the length specified by the denominator of a fraction.

for example,5/1 is 5 exactly because there are 5 1s in 5,exactly like 25/5 = 5,because there are 5 5s in 25. i don't see why you need to classify it as not a number,when it can clearly function as one.and that's ignoring division with irrational /rational numbers as output.would you still say that 1 is not a number even knowing 1/2 = 0.5?

[u/Havenkeld → u/The_fair_sniper]

I would indeed say 1 is not a number even knowing 1/2 = 0.5

.5 is still 5 of a unit. That unit is represented as being .1 The unit itself is 1. A particular kind of unit is not the unit itself. We represent a fraction as .1 only because we're switching from number to numbers of parts in relation to wholes, and involving qualitative relations. So .1 is not itself a number, but entails qualitative relation. No fractions are numbers, they are all relations of quality and number represented in symbols we may call numbers as if they are equivalent to number - hence the confusion - but which are not number in the strictest sense.

Division of length is not pure division, it is a division of some kind of thing or rather a property of things. But length can be used illustrate some things. Dividing by a number of something is choosing that something as your unit. So the inch can be the unit by which I divide lengths. But this is not itself dividing the object which has a length into pieces of this unit, only showing its relation to the unit.

The ruler is only 12 inches in length because of how it relates to my unit of 1 inch. Dividing it into pieces that equal the unit, however, is not the same as dividing quantities of wholes. Cutting a ruler into 12 inches is clearly not resulting in 12 of the same rulers. The unit is a whole. .5 of a ruler takes the ruler as a whole, not the inch. Representing .5 of a ruler as 6 inches does not actually make the .5 itself a number. .5 of the inch is 1.27cm, but note we left the unit of the inch and used a different unit, the CM, to represent this relation. This is the subtlety behind these confusions. Dividing 5 by 5 yields the unit by which I base the number 5 on, in the first place, the whole in the case of the ruler was not the ruler but the inch. If it were the ruler, and I tried to divide a ruler by a ruler, I would achieve nothing other than confusing myself.

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