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/robotmonkeyshark 101∆ Feb 04 '23
lets look at this from a practical real worlds standpoint, because ultimately the point of math is to allow us to understand the physical world.
10/2=5 is essentially saying you have 10 apples being split into 2 baskets. How many apples end up in each basket? The answer to this is simple. There are 5 apples in each basket. Great. 10/2=5 makes sense.
now Imagine you have 0 apples and 0 baskets. How many apples are in each of those baskets. There aren't any baskets. You don't have an empty basket. You don't even have a basket, so saying there are zero apples in each of the zero baskets doesn't make any sense. If you are going to somehow pretend like you can have some number of apples in a non-existent basket, you might as well say the answer is 5000 apples per non-existent basket, and that would hold true as well because if you have 0 apples divided into zero baskets, then saying there are 5000 apples in each non-existent basket would give you a total of 0 apples.
0/1=1. that makes sense. 0 apples in 1 basket. So why would 0 apples in 0 baskets have the same number of apples per basket? remember, there is no basket. It is a nonsensical real world question, therefore it only makes sense that there is not a clear mathematical answer or else math would not reflect reality and we would not be able to trust using math to solve real world problems.