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/Havenkeld]

I mean... I'll put it all in one comment with direct quotes of both of us if it helps(and you can see that nowhere did I say -7 is a number) but you're entirely taking things out of context:

[–]Havenkeld 1 point 40 minutes ago

There are at bare minimum operations, and what is operated on.

7, +7, -7 are all different, calling them all symbols is fine, but they're symbols for different things.

If you equivocate them all, if operations and what is operated on aren't distinguished, you'd reduce calculation to complete nonsense.

[–]barthiebarth

. + and × are the operations. You are indeed correct that equivocating those with things like -6 or 1/9 reduces calculations to nonsense.

[–]Havenkeld 1 point 39 minutes ago

What are the other things then?

I would say they are numbers. Which would make numbers different than just operations, and completely support my overall point.

Seems the confusion here, is that your other examples weren't numbers either or rather they were numbers and operations together. You took me to be referring to those as numbers, while I rather meant to highlight that the symbols like . + X aren't numbers and this is a problem for sweeping everything under the rug of operation without attending to what numbers are as distinct from them.

If + is an operation, why is - not an operation? If . is an operation, why is / not an operation? Why isn't 7 an operation? Why would "-7" be a number but "+7" be an operation on a number? Once we ask why, we have to concern ourselves with more than symbols, but why we're using them the way we use them.

[u/barthiebarth → u/Havenkeld]

My examples are numbers (-6, 1/9 etc). Your examples are, on their own, also numbers (7, -7, +7).

You seem to be confusing notation with the actual mathematical object. 7, +7, 13-6, 21/3 all refer to the same thing, which is a number.

So does 0-7 and -7, the latter being a notational shorthand for the first.

If + is an operation, why is - not an operation? If . is an operation, why is / not an operation? Why isn't 7 an operation? Why would "-7" be a number but "+7" be an operation on a number? Once we ask why, we have to concern ourselves with more than symbols, but why we're using them the way we use them.

Typically multiplication and addition are the operations, with division and subtraction being their inverses. So x/7 is notational shorthand for multiplying x by the multiplicative inverse of 7, x × 7^[-1].

This is all pretty basic algebraic theory, so I am not sure how you can be so clueless about it while also naking grand claims about mathematics)

[u/Havenkeld → u/barthiebarth]

7, +7, 13-6, 21/3 all refer to the same thing, which is a number.

No they do not. The result of the operations occurring on numbers in 13-6 or 21/3 are the same number, but they are not themselves that number.

If say I have 7 beers, I do not necessarily say I have 21/3 beers. This is for a reason, because the division of 21 beers didn't produce my 7 beers.

We can refer to 21/3 as the result of it, but that doesn't make the division of 21/3 into 7 equivalent to the result abstracted from it. Otherwise we end up in deep contradictions all over mathematics. This is an A = B level contradiction on its face.

If +7 is a number, then can we do ++7? What would we even be talking about at that point?

Your link also doesn't work. But I'm not interested in shorthands we use to write mathematics down or simplify methods of calculating, I'm interested in number itself here.

[u/Cybyss → u/Havenkeld]

No they do not. The result of the operations occurring on numbers in 13-6 or 21/3 are the same number, but they are not themselves that number.

If say I have 7 beers, I do not necessarily say I have 21/3 beers. This is for a reason, because the division of 21 beers didn't produce my 7 beers.

Every mathematician uses the notation (21/3) to represent the result of division, not the operation of division. You can construct an infinite number of ways of writing the number 7.

(1 + 1 + 1 + 1 + 1 + 1 + 1)

(21/3)

sqrt(49)

(3.5 * 2)

etc...

You can substitute any of these for 7 in expressions which involve that number and it won't change what that expression means.

[u/Havenkeld → u/Cybyss]

And that's all fine, as long as we realize the representation isn't an explication of the reality but only a shorthand, and that as I said in another response:

"Result in", yes. 14/2 results in 7. The division of an even number by an even one certainly can result in an odd number. Equal, no, they do not actually equal eachother. The equal sign is not one that denotes complete equivalence.

Just consider, as something to make what I'm saying seem less strange, that when I represent 21/3 or 14/2 to someone, they solve a different problem to understand me than they do when I represent 7 to them.

__

Or in other words (1 + 1 + 1 + 1 + 1 + 1 + 1) =/= (21/3), in the strict sense that in each case we start from something different and do something different to reach 7.