# 0 divided 0 = ?

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Who is this "Khan"?

"You’ve managed to kill just about everyone else, but, like a poor marksman, you keep missing the target."

Can I throw a can or worms at ya all???

say we have a table with a mirror.
On the table we have nothing and in the mirror we have a reflection of nothing.
So now we have zero plus a reflected zero,.
Questions:
1] By using a mirror have we just divided or multiplied the zero in to two zero's (0 = 0*2)
2] Can one say they are the same zero?
3] Does either zero, the source or reflection, still equal zero?
using a vertical line as a mirror symbol we could have the notation 0|0

(0|0) / 0 = ?

Seriously curious...

Extended:
Say we have two perfectly parallel mirrors and place zero [nothing] in between, do we essentially have an infinite number of reflected "unique" zeros or only one zero?

Hi Capt, Lakon.

Yes, you two have highlighted the illogic of dividing zero by any non-zero number. It is basically a 'non-starter' contrived situation, and not a serious action/process in any sense or system.

Hi Undefined; all I was saying, was that 0/0 is non-sense. I hadn't thought about 0/n, although thinking about it now and applying words to it, I have no apple, therefore, it stops there. Talk about dividing something I haven't got, be it by zero or any other number, to me, again seems non-sense.

@Lakon

..

With regard to the apple story.
When there is no apple to divide, and it is theoretically divided among zero pupils, the result is still no apple.
Yet mathematically, some people believe that zero divided by zero equals one.
That you get an apple from nowhere.

And from what I read earlier, you disagree with that. As do I.

I don't think I've seen anyone say 0/0 = 1 on this thread .. yet ..

If anyone does believe that, I would like to see how they arrive to such a conclusion.

Possibly but zero divided by zero is ONE. Binary computing simply does not have the capablility to perform such an equation, unless anyone has a different algorithmn to describe binary mathematics. *looks about*...

@Lakon
See above.

The reasoning is that if you divide any other number by itself, the result is 1.
But as the result is demonstrably wrong, that cannot be the case with zero.

So, RealityCheck, is of the opinion that zero is not a natural number.

OK, can he move to the philosophy section now?

Undefined: Since this thread keeps growing despite the fact that it was answered decisively on page 1, I finally went ahead and read your position. You seem to be claiming that we should treat zero as fundamentally different from other real numbers, more like a state of balance than a number. Is that fair? If so, then how could we use zero in math? Would you have to come up with a whole different set of rules describing how to do math with zero as opposed to doing math with other numbers? I'd be very curious to hear what those rules might be.

Quantum Quack: I think you're going about the problem backwards. If we have a mirror reflecting nothing, then that's a physical arrangement of objects, and it is what it is. It makes no sense to ask "whether the reflected zero is the same as the original zero" because the universe doesn't care about number systems; it just does physics, and we use number systems to describe and predict its behavior. Now if you put some units on the zeros, they might describe some property of the real system, in which case we could do math with them and get meaningful answers.

$$5^0=\frac{5^1}{5^1}=5^{1-1}=5^0=1$$

And just what does $$1-1=?$$

This is another perfect exemplar of the triviality route to 'proofs' which I already commented upon.

Consider the equally trivial: $$5^0=\frac{5^0}{5^0}=1$$

It gives the same "output" state without all the covering trivialities of "1-1" unnecessary manipulations of the number/exponent convention symbols to 'decompose' trivially a simple "0" state which existed fundamentally AS a "0" state to indicate the "non-action" or "instance/presence per se" condition of whatever base number was involved before all the trivial abstract manipulations I observed upon already.

The use of a convention for exponents using the zero just as trivially (ie, the 0 in 5^0 is trivially an indicator that there is only "1" state of the number "present", ie, the base value of "instance of a number" per se, rather than of any operation being applied to that number) is just another example where trivial self-selecting axioms/conventions and 'decompositions' and 'manipulations' etc only serve to hide the initial reality fundamental status of the actual number/symbol when not being 'hidden' by higher abstractions away from that fundamentality. It is these higher and higher abstractions away from real fundemantality that creates "undefined" situations which can be avoided if the fundamentality is recognized and treated appropriately (as I already suggested a new convention, keeping such things within parentheses and having regard to the contextual meaning of the "output" of "1" unitariness etc) and have regard to the context they are used in.

Thanks for your on-topic and interesting input to the discussion points, Beer w/Straw.

Edit: About your eagerness to characterize/dismiss the discussion points as "philosophy" and trying to tell the mods what is or is not acceptable issues/points for this thread in the context so far, Bw/S: mate, never lose sight of the fact that axioms/postulates start out in the realm of philosophy, and only afterwards do we proceed to follow the indicated logics and axiom-consistent abstractions (trivial and otherwise) based on the starting philosophically based initial axiom/postulate. It's all connected and complete, only our arbitrary abstractions/divisions make it seem disconnected (hence the stubborn "undefined" and "incompleteness" states peppering our current maths/physics status quo).

"You’ve managed to kill just about everyone else, but, like a poor marksman, you keep missing the target."

Thanks for the info. Haven't been much of a TV/movie follower. But it's interesting to note that even serious mathematicians/scientists have time to spare to become knowledgeable with what is happening with all those TV/movie characters! Not my cup of tea, so I didn't get that "Khan" jibe. Thanks, Pete.

Undefined: Since this thread keeps growing despite the fact that it was answered decisively on page 1, I finally went ahead and read your position. You seem to be claiming that we should treat zero as fundamentally different from other real numbers, more like a state of balance than a number. Is that fair? If so, then how could we use zero in math? Would you have to come up with a whole different set of rules describing how to do math with zero as opposed to doing math with other numbers? I'd be very curious to hear what those rules might be.

Hi Fednis48.

I didn't want to do more than just contribute my little humble observations/suggestions to the discussion of the OP and matters raised by respondents to same, mate. I have said all I have to say at this juncture, and I don't want to get into further details as I am busy working on my "contextual" maths system as well as my "complete, consistent" ToE from scratch.

If you re-read my posts/responses so far in this thread you will get the gist/thrust of my more exhaustive approach/suggestions which will be fully outlined when I publish the whole works. Until then, I am constrained to only post on specifics as already encountered in the thread discussion so far. If I start to expand further upon what new approaches/treatments are in the wind, it would take too much of my time which is desperately needed to finalize my works for publishing.

Anyhow, my latest post to Bw/S will give you a further hint as to the sort of thing which should be done to avoid the usual circuitous/trivial abstract 'proofing' devices, contrivances, methods which depend on 'trivial decompositions'; and on just as trivial 'unnecessary' intermediate manipulations which serve only to 'hide' and lose sight of the funadamentality of certain things/concepts (like zero, and like/like constructs/resultants etc etc)....which inevitably leads to such requirements to deem things axiomatically/logically "undefined" etc simply because we missed the fundamentality point right from the start/context before we let all our subsequent abstractions run away with themselves.

Thanks for your polite and intelligent discussions over the various threads, mate! Much appreciated, I assure you, and by more than just myself.

Have to leave now for a while. Don't know when I will be posting again. Good luck and enjoy your discussions, Fednis48, everyone!

Please don't misunderstand me. I have no argument against that stage or 'functions' per se. I only want to explore what is the reality treatment at its most fundamental levels in BOTH cases: ie, where zero is treated in any 'functions' context; and where zero is treated in any 'number' context.

I already have presented my own more fundamental arguments that zero is NOT a 'number' OR a 'function' of any kind. But rather it is a state or condition or symbol for origin etc etc invoking physical aspects such as 'superposition' and 'trivial action' effectively a NON-action (as I pointed out to rpenner that his separation of the zeros in "0/0" expression is trivial and not proper in view of the "Rules of evaluation of expressions" is properly invoked and maintained throughout for ANY "like/like" expression, including zero/zero if that ever arises).

So I am not pursuing the set theory stage/function arguments, just the most fundamental illogics which arise per se if/whenever zero is in reality context trivially/invalidly being attempted to be treated as 'a number' or manipulated trivially 'functionally' as I already pointed out to rpenner.

Please do carry on with your own set/function approach to your discussion with the OP et al. I have no argument with you so far, mate!

You are trying to defining your own mathematics without any valid definition.

In set theory, 0 has a precise definition.

$$\emptyset=\{x:x\neq x\}$$

and then zero is defined as

$$0\equiv\emptyset$$

RealityCheck,

OK $$5^0=\frac{5^1}{5}=\frac{5^1}{5^1}=5^{1-1}=5^0=1$$

Sorry, that would be more conventional. Clearly though, what you posted is different from what I posted. Are you following any convention? Could I construe that $$5^5=\frac{5^5}{5^5}=1$$ from your post just as easily?

And when I say that you are not of the opinion that zero is a natural number, it's OK really. Hint! Hint!

But Good luck with your Theory of Everything from scratch!

Hi chinglu.

I was just checking for egregious typos in my last few posts, when I noticed this...

You are trying to defining your own mathematics without any valid definition.

In set theory, 0 has a precise definition.

$$\emptyset=\{x:x\neq x\}$$

and then zero is defined as

$$0\equiv\emptyset$$

Briefly, because I haven't much time, the "contextual mathematics" system I am working out is designed to 'bridge' all the other axiomatic systems and the definitions they entail. Since the status axiomatically "undefined" occurs in the conventional systems, then it requires some 'overarching' approach to supply the missing connections which will make those "undefined" things no longer crop up. The way to do the 'bridging' is to bring the most problematic terms/expressions back to the most fundamental reality status "contextually" such that when all these other incomplete systems are re-interpreted and given context/place in the overarching system, their various "undefined" and other axiomatically problematic cases will be overcome and given an axiomatically consistent treatment via "contextual maths" system whenever the "limits of the domain of applicability" of the various conventional incomplete systems are encountered.

So I am not 're-defining' anything except how to treat things that are "undefinable" within the conventional systems, by the approach of a 'bridging system' via contextual treatment of the conventionally problematic bits as necessary.

My system will only 'intrude' in current definitional system whenever that current definitional system fails and outputs an "undefined" entity which must be brought back to its most fundamental status/context (hence the name "Contextual Mathematics") and assist current systems to avoid trivial/undefined situations altogether.

Gotta go! Bye and good luck and thanks for your own very interesting discussions/OPs, chinglu, everyone!

Quantum Quack: I think you're going about the problem backwards. If we have a mirror reflecting nothing, then that's a physical arrangement of objects, and it is what it is. It makes no sense to ask "whether the reflected zero is the same as the original zero" because the universe doesn't care about number systems; it just does physics, and we use number systems to describe and predict its behavior. Now if you put some units on the zeros, they might describe some property of the real system, in which case we could do math with them and get meaningful answers.
How then would you render in mathematics the reality of a zero dimensional void being reflected in a mirror(s)?
Does mathematics have a function that describes multiplication by reflection of self? [I am using a | symbol for the example below]
"A form of reflected equivalence"
re:
Can I throw a can or worms at ya all???

say we have a table with a mirror.
On the table we have nothing and in the mirror we have a reflection of nothing.
So now we have zero plus a reflected zero,.
Questions:
1] By using a mirror have we just divided or multiplied the zero in to two zero's (0 = 0*2)
2] Can one say they are the same zero?
3] Does either zero, the source or reflection, still equal zero?
using a vertical line as a mirror symbol we could have the notation 0|0

(0|0) / 0 = ?

Seriously curious...

Extended:
Say we have two perfectly parallel mirrors and place zero [nothing] in between, do we essentially have an infinite number of reflected "unique" zeros or only one zero?

Hi Bw/S, I almost missed this in my haste to log out.

OK $$5^0=\frac{5^1}{5}=\frac{5^1}{5^1}=5^{1-1}=5^0=1$$

Sorry, that would be more conventional. Clearly though, what you posted is different from what I posted. Are you following any convention? Could I construe that $$5^5=\frac{5^5}{5^5}=1$$ from your post just as easily?

And when I say that you are not of the opinion that zero is a natural number, it's OK really. Hint! Hint!

But Good luck with your Theory of Everything from scratch!

No, mate. The triviality is the 'like/like' construct. Your above constructions ($$5^0=\frac{5^1}{5}=\frac{5^1}{5^1}=5^{1-1}=5^0=1$$) and ($$5^5=\frac{5^5}{5^5}=1$$) have no basis at all, trivial or otherwise, since neither involves VALID immediate step expansion to 'like/like' situation.

ie,

Your expression/construct expansion $$5^0=\frac{5^1}{5}$$ has UNlike/UNlike construction/extension, so is irrelevant and illogical in any sense/system. Not consistent with what I was doing to illustrate my point/suggestion.

Your other expression/construct expansion $$5^5=\frac{5^5}{5^5}=1$$ creates an INVALID extension/construct of like/like from a stand-alone definitive number 5^5 which is NOT amenable to what you did "equating" it to the construct $$\frac{5^5}{5^5}=1$$, since it obviously does not equal one from the starting number 5^5.

I don't know what 'system' you are using, but it has nothing to do with what I or the conventional conventions agree with! Maybe you should start a project of your own and call it "Even More Weird Maths", just to see if your above attempts make any sense in some 'other universe' maybe?

Thanks anyway for interest and the good wishes, Bw/S. Gotta go. See ya round.

Your other expression/construct expansion $$5^5=\frac{5^5}{5^5}=1$$ creates an INVALID extension

Huh? Where did you get this nonsense?

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