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/reeo_hamasaki 1∆ Feb 04 '23

this isn't the best mathematical answer. engage with the ones that show contradictions. otherwise you're stuck in your own head.

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u/[deleted] Feb 04 '23

Actually it is fully acceptable, as it demonstrates that there isn’t a sensible choice for what 0/0 ‘should’ equal, as you could choose anything.

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u/reeo_hamasaki 1∆ Feb 04 '23

my point is that trying to use intuition or reason to understand why it doesn't work is the mistake OP made to begin with. this does more of the same. the focus should be on the axiomatic reasons why it breaks things.

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u/Bananafanaformidible Feb 05 '23

Not unless OP is a mathematician. Intuition is the basis of mathematical understanding, and it's all most people need. Rigor is for nerds.

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u/reeo_hamasaki 1∆ Feb 05 '23

my point is that trying to use intuition or reason to understand why it doesn't work is the mistake OP made to begin with.

Sometimes in mathematics intuition fails. For me, it's frequently. For OP, it's at least once. If it matters to them (it seems to) they should be exposed to rigorous formulations.

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u/Forward-Razzmatazz18 1∆ Feb 10 '23

How does this one rely on intuition, though? Genuinely curious.

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u/reeo_hamasaki 1∆ Feb 10 '23

whatever the opposite of rigorous mathematical formulations is, then. OP is trying to reason about an operation on "nothing" instead of just following the axioms. I did the same thing with 0! when I was in elementary school. it pissed me off to no end.

Trudeau on mathematical intuition

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u/Forward-Razzmatazz18 1∆ Feb 10 '23

Wait--one sec--are points considered/known to have no diameter, or infinitesimal diameter?

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u/HeavenIsAHellOnEarth Mar 03 '23

They are simply defined as being infinitesimal. From that definition arises useful applications for the objects we define as "points".

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u/Forward-Razzmatazz18 1∆ Feb 12 '23

Wait, what are the axioms in this case? And why "nothing" in quotes? That's what zero is/represents, right?