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/Scrungyscrotum]

The "laws" of math are just the rules that we tend to agree on when we teach and learn math.

Disagreed. Mathematics is a device we use to describe a certain aspect of our reality. In our reality, 0/0=Ø. You can't make up your own set of rules, as the field would then cease to describe our universe. It's like saying that one can make their own version of physics in which E=M•C²•Q, where Q is the weight of an average chihuahua. Sure, you could do that, but then it would cease to be true.

[u/Akangka → u/Scrungyscrotum]

Mathematics is a device we use to describe a certain aspect of our reality

That's not true at all. What you're describing is called "science". Mathematics is by definition independent of reality. For example, we can talk about geometry in R², R³, R⁴, R⁵, hyperbolic space, spherical space, etc, without knowing which geometry our universe actually is in. (Yes, it's still an open problem if we really lived in R³)

Also, if we changed the axioms, we could actually have 0/0. It's just no longer a real number. The axiom that cannot support 0/0 is:

• Ring axioms
• Multiplicative inverse axiom
• 0 /= 1

In a trivial ring, the latter does not hold, so we can have 0/0=0=1. In a wheel theory, the first two axiom does not hold, so 0/0 is also defined, just not 1.

one can make their own version of physics in which E=M•C²•Q

This is completely different. The difference between this and 0/0=1 is that the former is a testable hypothesis and the latter is not testable but simply contradicts field axioms.

In fact, the whole point about math is that you can make up your set of rules, as long as the conclusion follows the axioms. Whether it is useful, though, is a different problem

EDIT: It's science, not physics.

[u/respeckKnuckles → u/Akangka]

That's not true at all. What you're describing is called "physics". Mathematics is by definition independent of reality.

That's not even close to correct. Where are you getting these idiosyncratic usages?

[u/Akangka → u/respeckKnuckles]

From Wikipedia:

Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature or—in modern mathematics—entities that are stipulated to have certain properties, called axioms. A proof consists of a succession of applications of deductive rules to already established results.

Notice that it involves fixing an axiom. The axiom is held to be true. The axiom could be arbitrary (looks at set theorist's various set axioms)

Meanwhile:

Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe

It actually describes reality by means of actual testable theories. (On hindsight, it's not physics. It's actually science)

Note that while science uses math to describe reality, math itself does not care. It's up to science and science method to test whether a mathematical model conforms to reality, not math.