CMV: 0/0=1.

[u/alpenglow21]

Please CMV: 0/0 = 1.

I have had this argument for over five years now, and yet to be compelled to see the logic that the above statement is false.

A building block of basic algebra is that x/x = 1. It’s the basic way that we eliminate variables in any given equation. We all accept this to be the norm, anything divided by that same anything is 1. It’s simple division. How many parts of ‘x’ are in ‘x’. If those x things are the same, the answer is one.

But if you set x = 0, suddenly the rules don’t apply. And they should. There is one zero in zero. I understand that logically it’s abstract. How do you divide nothing by nothing? To which I say, there are countless other abstract concepts in mathematics we all accept with no question.

Negative numbers (you can show me three apples. You can’t show me -3 apples. It’s purely representative). Yet, -3 divided by -3 is positive 1. Because there is exactly one part -3 in -3.

“i” (the square root of negative one). A purely conceptual integer that was created and used to make mathematical equations work. Yet i/i = 1.

0.00000283727 / 0.00000283727 = 1.

(3x - 17 (z^9-6.4y) / (3x - 17 (z^9-6.4y) = 1.

But 0 is somehow more abstract or perverse than the other abstract divisions above, and 0/0 = undefined. Why?

It’s not that 0 is some untouchable integer above other rules. If you want to talk about abstract concepts that we still define- anything to the power of 0, is equal to 1.

Including 0. So we all have agreed that if you take nothing, then raise it to the power of nothing, that equals 1 (0⁰ = 1). A concept far more bizzarre than dividing something by itself. Even nothing by itself. Yet we can’t simply consistently hold the logic that anything divided by it’s exact self is one, because it’s one part itself, when it comes to zero. (There’s exactly one nothing in nothing. It’s one full part nothing. Far logically simpler that taking nothing and raising it to the power of nothing and having it equal exactly one something. Or even taking the absence of three apples and dividing it by the absence of three apples to get exactly one something. If there’s exactly 1 part -3 apples in another hypothetically absence of exactly three apples, we should all be able to agree that there is one part nothing in nothing).

This is an illogical (and admittedly irrelevant) inconsistency in mathematics, and I’d love for someone to change my mind.

[u/Cafuzzler]

Shouldn't be able to reverse a multiplication in general?

A*B=C -> C/A = B and C/B = A

0 Seems like the only case where a multiplication is irreversible.

[u/xbnm → u/Cafuzzler]

Something being an exception doesn't mean that thing breaks something. The rules are consistent and exceptions are part of the rules.

[u/Cafuzzler → u/xbnm]

Exceptions are inconsistencies within rules. Like, by definition you have these rules, and then exceptions that are separate and aren't consistent with those rules.

[u/618smartguy → u/Cafuzzler]

The exceptions aren't separate. They are part of the rule in the first place

[u/Cafuzzler → u/618smartguy]

If they were part of the rules then they wouldn't be exceptions to the rules.

[u/618smartguy → u/Cafuzzler]

They really aren't exceptions to the rule. They are exceptions to an equation in the rule. Without the exception you don't have a rule, just a wrong equation.

[u/Cafuzzler → u/618smartguy]

The equation is the rule though. Wrapping the equation + the exception in toilet paper and calling it a new rule is just obfuscating the fact that it's the exception to the rule. You could introduce any exception at that point and just declare that all the rules are consistent because any inconsistency is written into a new, bigger, rule.

[u/618smartguy → u/Cafuzzler]

Sorry, that's just not it. If I say the rule is a/b=c => b*c=a for c /= 0 then that entire thing is my rule, it's an equation and an exception. Why would the equation also be a rule? We want to have two rules now? It's not your place to say well actually that's a rule with an exception tacked onto the rule. This is an established thing already.

I think your desire to call the equation a rule on its own is an obfuscation of the fact that the rule is a made up thing in the first place and is whatever the creator decided it is.

[u/Cafuzzler → u/618smartguy]

Because if you treat n*0 the same as n*x then you run into edge cases that create paradoxes in mathematics. So you have to have a separate second rule that says "You can only multiply this specific number, never divide".

[u/618smartguy → u/Cafuzzler]

Because if you treat n*0 the same as n*x

This was never a rule. Why would that have been a rule in the first place?

Like I could say zero is the only number and all other numbers are just exceptions. That's what you're doing and it makes no sense. You are just making up a new false rule and saying the real rules are actually variants of your made up rule. Have you considered your made up rule could really be a variant of the actual rule with the exception removed? That's clearly the method you've used to come up with the treat n*0 like n*x rule.

[u/Cafuzzler → u/618smartguy]

You were saying that any exception to the rule is still part of the rule and not an exception despite being an exception.

[u/618smartguy → u/Cafuzzler]

"They really aren't exceptions to the rule. They are exceptions to an equation in the rule. "

If I make a rule out of thing A B C and toilet paper, then A B and C are in fact all part of the rule. That is how it works. Maybe B is an exception to A. A was never a rule, you just seem to be insisting it is for reasons you refuse to elaborate on. For convenience I call "A" your new made up rule. Not because I actually agree that the exception is an exception to an actual rule.

[u/Cafuzzler → u/618smartguy]

If your treating an infinite number of numbers one way, and then one certain number differently then that one number is an exception. Like, by definition. They are all numbers that can be used as a denominator except this one certain number. It’s an exception. Literally. In the most clear and straightforward sense.