Zero divided by Zero equals 0 & 1 & ∞

What is the basis for reason? And mathematics?

Moderators: AMod, iMod

Scott Mayers
Posts: 2446
Joined: Wed Jul 08, 2015 1:53 am

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Scott Mayers »

Jaded Sage wrote:I suppose that is part of the issue then. Why is an exception made for zero?
Because the solutions are multiple. This is alright but it would no longer 'function' if used in some finite way because it would never fix on one number by the same rules. A number is a thing, like a noun. Infinity is like an unending action, like a verb. So while it works logically to think of it as a 'finite' kind of thing, it requires defining the action of unending solutions using a different term. A gerund in language turns an infinite verb, like "to walk" into a noun, like "walking". We also colloqually say, "I am going for a walk," to do this too. But to be consistent to the rest of the normal definition of "division of a number", requires using numbers for both domain and range. Infinity, while it is also used, is considered not defined or simply, "infinite", which means a similar thing.

Technically, the answer you are seeking is this:

R = {x | -∞ < x <∞}, where R stands for all Real numbers.
Jaded Sage
Posts: 1100
Joined: Mon Aug 24, 2015 2:00 pm

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Jaded Sage »

I'm sorry, dude. I'm still not getting it.
Obvious Leo
Posts: 4007
Joined: Wed May 13, 2015 1:05 am
Location: Australia

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Obvious Leo »

Scott Mayers wrote: A number is a thing, like a noun.
Yes. A number is like a noun but this means a number is NOT a thing. It has no meaning without a referent.
Obvious Leo
Posts: 4007
Joined: Wed May 13, 2015 1:05 am
Location: Australia

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Obvious Leo »

To which I meant to add. Therefore zero is not a number, a fact which has been well understood in mathematical philosophy since time immemorial. Zero is a placeholder.
Scott Mayers
Posts: 2446
Joined: Wed Jul 08, 2015 1:53 am

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Scott Mayers »

Obvious Leo wrote:
Scott Mayers wrote: A number is a thing, like a noun.
Yes. A number is like a noun but this means a number is NOT a thing. It has no meaning without a referent.
No, numbers are a quantifying adjective if one wants to be more precise where it quantifies some UNIT as the noun. But this unit can be an infinity of things, including number itself. A unit of 1 count, for instance.

[Number]->(Unit)

And since an adjective with its unit describe a new noun, The above combination IS a noun and thus a thing or event.

So,
Obvious Leo wrote:To which I meant to add. Therefore zero is not a number, a fact which has been well understood in mathematical philosophy since time immemorial. Zero is a placeholder.
You mean time infinite? And infinite = 0/0! or "00" To assume an infinite things, you can't leave out the infinite things that are also NOT real, right? So even given your own belief that zero is NOT a number, it has to exist if you accept an infinity to exist. OR...if you don't accept infinity as real either, as it is less considered a number than even zero itself, as it cannot be contained and zero at LEAST acts as something as a place-holder, then you have to abandon using it to describe your idea of 'time'. What is time if it cannot be quantified?
Scott Mayers
Posts: 2446
Joined: Wed Jul 08, 2015 1:53 am

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Scott Mayers »

Jaded Sage wrote:I'm sorry, dude. I'm still not getting it.
Maybe you can help narrow down what you are not understanding? I don't know what you know or don't know enough to try to argue from your vantage point.
Jaded Sage
Posts: 1100
Joined: Mon Aug 24, 2015 2:00 pm

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Jaded Sage »

Mostly I don't understand the different expressions like the one with R. It's been a decade since I took math.
Obvious Leo
Posts: 4007
Joined: Wed May 13, 2015 1:05 am
Location: Australia

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Obvious Leo »

Scott. Zero is bad enough but infinity is even worse. Zero and infinity are both unrealisable mathematical abstractions which have no analogue in a physically real world. They can be used to describe the way a physical system TENDS but they can make no truth statements about the actual physical state of a system. This is why Newton's classical mathematics are the wrong tools to model a quantised and dynamic reality.
Jaded Sage
Posts: 1100
Joined: Mon Aug 24, 2015 2:00 pm

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Jaded Sage »

Ha, nevermind. I get that one. There are these little phrases that keep popping up in your explanations, tho. They keep jumping out at me saying, "Yeah, that's the problem or point I'm trying to make." You'll have to forgive me. It will be weeks before I'm able to engage in this subject wholeheartedly.
Scott Mayers
Posts: 2446
Joined: Wed Jul 08, 2015 1:53 am

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Scott Mayers »

Obvious Leo wrote:Scott. Zero is bad enough but infinity is even worse. Zero and infinity are both unrealisable mathematical abstractions which have no analogue in a physically real world. They can be used to describe the way a physical system TENDS but they can make no truth statements about the actual physical state of a system. This is why Newton's classical mathematics are the wrong tools to model a quantised and dynamic reality.
But you missed the point. I know you take 'time' as all that is necessary as a starting point in your view. However, since you also imply no origin to the universe nor end, this requires the idea of quantification of infinities and zeros. And defeating Newton doesn't help you either. Einstein adopted time as a fourth dimensional factor as do all cosmologists to this day as a static 'dimension'. (I'm still not sure what precisely you are meaning by "Newtonian"?)
Obvious Leo
Posts: 4007
Joined: Wed May 13, 2015 1:05 am
Location: Australia

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Obvious Leo »

Scott Mayers wrote:However, since you also imply no origin to the universe nor end, this requires the idea of quantification of infinities and zeros
Since I've just explicitly stated that these abstractions are not quantifiable you'll have to support this bizarre assertion with an argument.
Scott Mayers wrote: Einstein adopted time as a fourth spatialdimensional factor
I put in the important adjective you forgot. In the spacetime paradigm, as modelled by Minkowski in SR, time is explicitly a spatial dimension. This is transparent bullshit since spatial dimensions are bi-directional co-ordinate systems and the arrow of time points resolutely from the past to the future via the nexus of the present. The equations of physics are certainly time invariant but reality is stubbornly NOT.
Scott Mayers wrote:(I'm still not sure what precisely you are meaning by "Newtonian"?)
On this occasion I was referring specifically to Newton's classical calculus and its assumption of an infinitely divisible reality. That reality is infinitely divisible has been known to be bollocks since the pre-Socratics and this is why the models of modern physics are only probabilistic ones. A quantised universe cannot be modelled in this way, which is why these models are riddled with paradoxes and counter-intuitive absurdities as well as being mutually exclusive.
Philosophy Explorer
Posts: 5621
Joined: Sun Aug 31, 2014 7:39 am

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Philosophy Explorer »

If an entity (e.g. 0 or a negative number) obeys the axioms of algebra, that's enough for me to recognize that entity as a number so 0 does count as a number for me.

PhilX
User avatar
Greta
Posts: 4389
Joined: Sat Aug 08, 2015 8:10 am

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Greta »

Zero only exists in reality in a relative sense, eg. you have two apples, take five away and you have none. That means you have zero apples in the approximate place and time where there were once five.

However, "zero apples" is an imaginary concept because apples do exist. Somewhere, at some time. There may be zero apples in the basket now but there are apples somewhere, or there were. Zero is ultimately relative because there exists something rather than nothing.

Only if apple trees go extinct will there be truly zero apples, but even that it depends on time and place. Zero's relative truth and ontological unreality creates this kind of confusion.

So it's a nonsense to divide by zero in reality, effectively asking how many nothings make something, but theoretically the answer is ∞. By the same token, dividing by ∞ only equals 0 theoretically because no entity can be practically divided into infinite portions.
Obvious Leo
Posts: 4007
Joined: Wed May 13, 2015 1:05 am
Location: Australia

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Obvious Leo »

Greta wrote:Zero only exists in reality in a relative sense, eg. you have two apples, take five away and you have none. That means you have zero apples in the approximate place and time where there were once five.

However, "zero apples" is an imaginary concept because apples do exist. Somewhere, at some time. There may be zero apples in the basket now but there are apples somewhere, or there were. Zero is ultimately relative because there exists something rather than nothing.

Only if apple trees go extinct will there be truly zero apples, but even that it depends on time and place. Zero's relative truth and ontological unreality creates this kind of confusion.

So it's a nonsense to divide by zero in reality, effectively asking how many nothings make something, but theoretically the answer is ∞. By the same token, dividing by ∞ only equals 0 theoretically because no entity can be practically divided into infinite portions.
This is the way zero and infinity have traditionally been regarded in all the major schools of mathematical philosophy. Because no referent can be applied to them they have no ontological status.
Scott Mayers
Posts: 2446
Joined: Wed Jul 08, 2015 1:53 am

Re: Zero divided by Zero equals 0 & 1 & ∞

Post by Scott Mayers »

NOTE: Contrary to what you might be thinking, I just want to assure you that while I may disagree with your own stance Leo, I appreciate you and your own intelligence. So don't interpret any disagreement as any indicator of disapproval of you the person but only to my own 'perception' of your particular responses. It's nice to see you writing here ... and Merry Christmas to you and others if I forget to say it later.
Obvious Leo wrote:
Scott Mayers wrote:However, since you also imply no origin to the universe nor end, this requires the idea of quantification of infinities and zeros
Since I've just explicitly stated that these abstractions are not quantifiable you'll have to support this bizarre assertion with an argument.
This is odd. If you declare by definition that

What one unique thing is NOT true for me, call is X == there is no such thing as a quantifiable entity such as zero because it is "abstract" and then

What is 'abstract' == anything that is spoken of that is not true,

you are merely begging that what you don't like personally or can make sense of, you simply define it out of existence. You may as well say,

Definition: Anything Scott Mayers says that doesn't appeal to Obvious Leo == not true for Obvious Leo.

You stated above, "This is why Newton's classical mathematics are the wrong tools to model a quantised and dynamic reality." The word 'quantised' means anything that is discretely defined by a number. Yet you deny that any number is real to nature because it is itself an abstraction. I demonstrated that it acts adjectively to define a unit, which itself is equally an abstraction to which you place anything you want in it, including something that you DO agree is real. Thus, you can define the unit, a particular apple that you see. Would you assert that since the apple is 'quantised', as being a "quantity" of ONE (number '1' abstract measure), that it too is unreal? You cannot escape the circularity of your own reasoning here. Say that not even the idea of ONE is true, since it is an abstraction. Then you can NEVER appropriately generalize anything as you'd have to treat each and everything as absolutely unique.

That is, you could never say, "I have two apples", and expect this to be real without accepting that 'two' has a meaning as well. You might have to say "I have this apple and something else that I cannot name." That is, you cannot use the term 'apple' again to even count them because to you there is no meaning to number. If you even say, "I have appleapple" to indicate two, this might work but would you not say that there is anything that you could generalize symbolically that represents the reality of whether you have 'two apples' or not?

Quantity is real. But it is a form(ula) type of word that requires a variable which you place after it to make any sense of it. Yet unless even the object you replace it with is not even allowed the concept of ONE to define it, than the word, "unique" (ONE of a kind), is useless too.

I cannot 'prove' to you anything because you defined OUT by default this capacity to do so with you regardless. You have implicit definitions of things which you will not bend on AND yet you also still insist on using with contradiction. You cannot accept that numbers don't mean anything 'real' but then selectively use the phrase, "everything is quantised", as it means something more true. Try taking out numbers all together in your language just to see how impossible it is to communicate without them. Should this NOT prove to you that numbers are more than mere 'abstractions' or falsities?

I recognize your reasoning is NOT unique. I understand, for instance how the acceptance of zero itself was vehemently fought against time and time again. Christianity, for instance ignored the year '0' as they couldn't believe it true. So to them, that first year was also '1' plus the days past the initiation of that year.

But you also deny time as having two directions. If this was the case, you could never speak of ANY past of your present as even had existed. What would it mean to say 10 years ago if not to simple mean -10 from your present, where your 'present' is always the assigned ZERO. If you started from 1, then does 10 years ago mean 9 of our years ago, without a real zero? In the symbol for "10", '0' is a place holder but means Zero ONES. You also don't KNOW the future other than your present. So I can argue that '0' is all you ever 'know'.

This is at least some 'argument' you ask for but I don't believe it will be qualified for you because of what I've said.
Scott Mayers wrote: Einstein adopted time as a fourth spatialdimensional factor
I put in the important adjective you forgot. In the spacetime paradigm, as modelled by Minkowski in SR, time is explicitly a spatial dimension. This is transparent bullshit since spatial dimensions are bi-directional co-ordinate systems and the arrow of time points resolutely from the past to the future via the nexus of the present. The equations of physics are certainly time invariant but reality is stubbornly NOT.
Actually, if you want to be accurate, the point, itself without lines IS this idea that you are thinking of. That is, a point, rather than a line, is the ZEROTH dimension and what you are interpreting about time since from anything that is not a point is a 'ray' which defines this concept. But we understand this NOT to be 'time' but a static point or place to which anything else but it defines the rest of reality.

"Space-time" is appropriate for the fourth dimension as it both explains the fact that space expands (ie, changes) and gives rise to time from an eternal static state of a point. One unit expansion per 'second' represents both the Volume of additional space of expansion AND this in turn requires change of one set or frame of a three-dimensional world to BECOME another. Time is thus like the mathematical measure of differences of static three-dimensional pictures.
Scott Mayers wrote:(I'm still not sure what precisely you are meaning by "Newtonian"?)
On this occasion I was referring specifically to Newton's classical calculus and its assumption of an infinitely divisible reality. That reality is infinitely divisible has been known to be bollocks since the pre-Socratics and this is why the models of modern physics are only probabilistic ones. A quantised universe cannot be modelled in this way, which is why these models are riddled with paradoxes and counter-intuitive absurdities as well as being mutually exclusive.
I see that you have a problem with infinities. But if zero and infinity are the minimal of what you accept, I'm guessing that you have to at least accept ONEness no matter what. At least, without any standard, you cannot make any sense of any number of things at all. I think that it might help if you prefer to define no number 'real' how would you begin to describe anything? Even 'time' means nothing without contrasting it between at least "two" different experiences. And here, this 'unit' (a oneness) would be "experience". If you follow my concern, can you explain how you could understand anything without inferring that number has a real meaning?
Post Reply