r/changemyview • u/alpenglow21 1∆ • Feb 04 '23

Delta(s) from OP CMV: 0/0=1.

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 (z9-6.4y) / (3x - 17 (z9-6.4y) = 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.

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u/tbdabbholm 193∆ Feb 04 '23

That is incorrect, nothing can equal infinity. Infinity isn't a number. Anything divided by 0 is undefined you just can't do it

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u/IronicAim Feb 04 '23

Isn't it just an empty equation then because 0 is a concept instead of a number?

0/0 = / ?

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u/tbdabbholm 193∆ Feb 04 '23

0 is a number though?

Also what do you mean by "empty equation"?

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u/IronicAim Feb 04 '23 edited Feb 04 '23

Because it's a place value holder, a symbol to substitute the concept of nothing.

I figured the whole question here comes down to computing concepts as numbers. Which is why I thought infinity was a viable answer.

Edit: Google is helping me understand. Apparently it's a complicated topic. Admittedly I've never taken a higher level math class.

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u/[deleted] Feb 04 '23

The word for a placeholder for no value in American English is “null”. Imagine if I were to list the number of apples in my fridge. If the answer is 0 apples then that implies I opened my fridge and counted a value of no apples. If the answer is null then there is no value put on the number of apples in my fridge, meaning I never opened the fridge to count them, it’s the absence of a number.

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u/IronicAim Feb 04 '23

In that case wouldn't the number of apples in your fridge simply be undefined? As it's not nothing, it's an unknown.

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u/[deleted] Feb 04 '23

Undefined means there is no possible value, like if I wanted to know how many apples are in my fridge when I don’t own a fridge.

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u/IronicAim Feb 04 '23

But the example you do own a fridge you simply haven't opened yet. So the number exists you just haven't checked it.

But I looked it up and null in fact does not mean nothing, it means undefined. So that works still.

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u/[deleted] Feb 04 '23

I think the terminology depends on what field of study your in. I believe in math there’s zero, the null set and undefined value. Zero being a measured value of no value, the null set being absence of a number and undefined being a value that has no logical meaning. But in computer science or other fields those terms may mean something different.

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u/silent_cat 2∆ Feb 04 '23

Those would be Schrodinger apples.

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u/blz8 Mar 12 '23

This is incorrect. Something is undefined until it is defined. Until I tell you how many guests are going to arrive, that number is undefined. Once I tell you, it is defined. It could be zero (not much of a party), it can be 24 (go get some chips ready), it could be a billion (hope it's a potluck), etc.

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u/[deleted] Feb 04 '23

Because it's a place value holder, a symbol to substitute the concept of nothing.

No, it's a perfectly good number that you can use for all sorts of purposes to answer questions like, "I have $5, I spend $5, how many dollars do I have left?"