First of all, it has nothing to do with the operation. If division was possible between zero's, it would happen clearly. This question has to do with numerology since the greater part of posters seem to recognize any number divided by a number results in unity. You can have limits. Sure. But this isn't the crux of why something cannot divided by zero. You cannot divide by zero because you are working already in a series of numbers and whilst zero is considered a number, it is best to think of it as no quantity at all. You cannot divided a real number by a pseudo-number. You cannot divided nothing by something, no more you can divide a real set of numbers by something which is infinite. You can not define a real number by an undefined operation. Zero literally means, zero. It is nothing, it does not hold the same class as the real numbers in which real quantities are defined.
0 divided 0 = ?
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Hi chinglu.
I was just checking for egregious typos in my last few posts, when I noticed this...
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!
The undefined crops up in set theory when a contradiction is present. That is also called non-functional. This is excluded from set theory because it does not allow contradictions within the theory. Otherwise, it would be inconsistent.
That is why 0/0 is not defined/included as valid in set theory. It is that simple.
Hi Bw/S. Not much time again today, so briefly...
That $$x={x^1}$$ expression is yet another trivial 'unnecessary labeling' manipulation, and not a valid operation 'action' at all, simply because it is fundamentally superfluous to write "$$x$$" as "$${x^1}$$". It is trivially true that $$x={x^1}$$, so no fundamental gains are made by writing it out that way to trivially suit purely trivial 'proofs' exercise in futility for the sake of triviality instead of pursuing real fundamental insight 'in context' of reality and not for the sake of merely more sterile abstractions.
And the expressing of "0" as the output of a trivial "like-like" (ie, 1-1=0) is no justification for making trivial 'proofs' trivial manipulations/notations which only confirm the triviality whilst hiding the fundamentalities involved from the start.
Are you getting the drift about how the TRVIAL higher abstractions and manipulations are effectively hiding the fundamentality of the entities involved, and so effectively leading inevitably to axiomatically "undefined" situations which could have been proactively obviated by proper application of the 'bridging' suggestions and 'contextual math' treatments/recognition of the fundamentalities BEFORE going into the higher abstractions/treatments which (if not 'strictly constrained to reality context' as per my humble suggestions) will inevitably result in TRIVIAL and unnecessarily obfuscation of the fundamental properties of the entities involved, and so lead to "undefined" situations (which, again, could so easily be avoided from the start, as per my humble suggestions already put)?
Have to go again. Bye Bw/S, and thanks again for your sincere interest and politeness of late.
Not much time again today, so briefly...That $$x={x^1}$$ expression is yet another trivial 'unnecessary labeling' manipulation, and not a valid operation 'action' at all, simply because it is fundamentally superfluous to write "$$x$$" as "$${x^1}$$". It is trivially true that $$x={x^1}$$, so no fundamental gains are made by writing it out that way to trivially suit purely trivial 'proofs' exercise in futility for the sake of triviality instead of pursuing real fundamental insight 'in context' of reality and not for the sake of merely more sterile abstractions.
And the expressing of "0" as the output of a trivial "like-like" (ie, 1-1=0) is no justification for making trivial 'proofs' trivial manipulations/notations which only confirm the triviality whilst hiding the fundamentalities involved from the start.
Are you getting the drift about how the TRVIAL higher abstractions and manipulations are effectively hiding the fundamentality of the entities involved, and so effectively leading inevitably to axiomatically "undefined" situations which could have been proactively obviated by proper application of the 'bridging' suggestions and 'contextual math' treatments/recognition of the fundamentalities BEFORE going into the higher abstractions/treatments which (if not 'strictly constrained to reality context' as per my humble suggestions) will inevitably result in TRIVIAL and unnecessarily obfuscation of the fundamental properties of the entities involved, and so lead to "undefined" situations (which, again, could so easily be avoided from the start, as per my humble suggestions already put)?
Have to go again. Bye Bw/S, and thanks again for your sincere interest and politeness of late.
Hi Tach, welcome back from your ban. It seems you have not learned about the perils for you when you don't bother to read the full context before also excerpting isolated snippets out of that context and attacking the WRONG thing which such habits of yours have been leading you to which have got you the bans in the first place.
If you had done the right thing, you would have realized that these 'snippets' you fixated on...
...were merely QUOTING of Beer /Straw's examples/constructions to discuss the points raised by me which clearly point out the invalidity of above said examples HE used, not me. Ok, Tach?
Just in case anyone else is misled by your 'bad faith habits' against fair discourse (which habits have in the past confused threads/discussions sometimes to the point where the only option for the mod has been to give you a ban for it), here is the full context in my post you snipped the bits from, where I show clearly that those examples by Beer w/Straw were 'nonsense' (at least we do agree on that, Tach! )....
I trust that you and everyone sees now that those 'snippets' were not 'offered' by me, but Beer w/Straw; and that I only quoted them in my reply to his 'offerings'? Thanks.
PS: Tach, while I am glad to see your return, I would b even more glad if you had used your ban period to consider correcting your 'bad faith habits' which got you banned in the first place. Good luck in that apparently difficult personal endeavor for you. In any case, no hard feelings or grudges should be brought into future exchanges, from either end, hey? Good luck, Tach!$$
If you had done the right thing, you would have realized that these 'snippets' you fixated on...
$$
...were merely QUOTING of Beer /Straw's examples/constructions to discuss the points raised by me which clearly point out the invalidity of above said examples HE used, not me. Ok, Tach?
Just in case anyone else is misled by your 'bad faith habits' against fair discourse (which habits have in the past confused threads/discussions sometimes to the point where the only option for the mod has been to give you a ban for it), here is the full context in my post you snipped the bits from, where I show clearly that those examples by Beer w/Straw were 'nonsense' (at least we do agree on that, Tach!
)....Hi Bw/S, I almost missed this in my haste to log out.
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.
I trust that you and everyone sees now that those 'snippets' were not 'offered' by me, but Beer w/Straw; and that I only quoted them in my reply to his 'offerings'? Thanks.
PS: Tach, while I am glad to see your return, I would b even more glad if you had used your ban period to consider correcting your 'bad faith habits' which got you banned in the first place. Good luck in that apparently difficult personal endeavor for you. In any case, no hard feelings or grudges should be brought into future exchanges, from either end, hey? Good luck, Tach!
$$
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Understood long since, mate. No argument from me on that.
However, that elucidates my point about 'incomplete' axiomatic systems, of any kind, which produce undefined situations. The same applies to physical postulate systems which also lead to 'unknown' situations because of their in completeness due to domains of applicability 'gaps' prevent full and complete evolution from the start.
It is my 'bridging insights' and 'contextual treatments' for both mathematical axiomatic systems and physical postulatory systems which may help to forestall from the very starting stages (axiomatic/postulatory stages) all those 'undefined' and 'unknown' situations currently bedeviling the conventional (perforce inherently and inevitably 'incomplete') approaches to maths/physics system construction/evolution.
So far, my approach seems tobe the only way I have found that might possibly, just possibly, be a way around the various INCOMPLETENESS theorems which would have it as 'impossible' for any system to be 'complete' based only on its starting set of axioms/postulates alone.
See? My interest is in 'bridging' all those PARTIAL maths/physics systems, not 'replacing' them. I already recognize their limitations (ie, hence the undefineds/unknowns etc), but I am going 'outside' them in order to 'bridge' them from an overarching reality context angle which will not have any undefineds/unknowns in that overarching system. That is the goal, mate. I have no arguments to make against the specific 'functions' and 'set theory' etc issues you and rpenner et al were discussing.
Good luck to you, chinglu, rpenner et al in your own discussion points! Bye for now.
Understood long since, mate. No argument from me on that.
However, that elucidates my point about 'incomplete' axiomatic systems, of any kind, which produce undefined situations. The same applies to physical postulate systems which also lead to 'unknown' situations because of their in completeness due to domains of applicability 'gaps' prevent full and complete evolution from the start.
It is my 'bridging insights' and 'contextual treatments' for both mathematical axiomatic systems and physical postulatory systems which may help to forestall from the very starting stages (axiomatic/postulatory stages) all those 'undefined' and 'unknown' situations currently bedeviling the conventional (perforce inherently and inevitably 'incomplete') approaches to maths/physics system construction/evolution.
So far, my approach seems tobe the only way I have found that might possibly, just possibly, be a way around the various INCOMPLETENESS theorems which would have it as 'impossible' for any system to be 'complete' based only on its starting set of axioms/postulates alone.
See? My interest is in 'bridging' all those PARTIAL maths/physics systems, not 'replacing' them. I already recognize their limitations (ie, hence the undefineds/unknowns etc), but I am going 'outside' them in order to 'bridge' them from an overarching reality context angle which will not have any undefineds/unknowns in that overarching system. That is the goal, mate. I have no arguments to make against the specific 'functions' and 'set theory' etc issues you and rpenner et al were discussing.
Good luck to you, chinglu, rpenner et al in your own discussion points! Bye for now.
You are not getting it.
0/0 is not a problem in set theory. It is non-functional.
Why would this be a good thing in your "enhanced system"?
Because all these questions of 'non-functionality' and 'undefined' etc etc would be forestalled from the starting stage. So those questions/things don't arise or cause arguments when they arise in partial systems, they would be 'referred back' in reality context to the most fundamental entities in the overarching system approach I allude to which 'bridges' any axiomatic 'hiccups' in any one partial system.
I can't say any more than that at this time, mate. Good luck with all your discussions.
PS: No time left. Logging out now. Bye and enjoy your discussion on "0.9999999..." topic, mate. I only had time to contribute a brief two-cent's worth. I will read-only the evolving discussion with interest. Bye!
Sorry, RealityCheck, where I was following basic exponential rules, you were fumbling to make anything fit. That doesn't look well for someone writing a "contextual maths system" for your "complete, consistent ToE from scratch".
If you had stopped to think for just a bit, all I originally asked was:$$1-1=?$$
You latched on to my exponential manipulation, simply used to teach how $$x^0=1$$ provided $$x$$ doesn't equal zero, for whatever reason.
I mean look closely at$$5^0=\frac{5^1}{5}=\frac{5^1}{5^1}=5^{1-1}=5^0=1$$
It says:$$5^0=5^0$$ That's awesome mathematical prowess if you ask me!
You're writing a complete Theory of Everything but can't recognize basic exponential rules?
Good luck with that. But do tell why you got so tied up with my random post, or is it just that you really like to type long meaningless posts and pretend you're being smart?
If you had stopped to think for just a bit, all I originally asked was:$$1-1=?$$
You latched on to my exponential manipulation, simply used to teach how $$x^0=1$$ provided $$x$$ doesn't equal zero, for whatever reason.
I mean look closely at$$5^0=\frac{5^1}{5}=\frac{5^1}{5^1}=5^{1-1}=5^0=1$$
It says:$$5^0=5^0$$ That's awesome mathematical prowess if you ask me!
You're writing a complete Theory of Everything but can't recognize basic exponential rules?
Good luck with that. But do tell why you got so tied up with my random post, or is it just that you really like to type long meaningless posts and pretend you're being smart?
And you missed that I did see exactly what you were doing.
That is why your 'offerings' (rightly labeled "nonsense" by Tach) were quoted back at you while your triviality was made evident.
So you you obviously missed that your 'offerings' were TRIVIALLY based and constructed. They showed nothing extra than the trivially true status to begin with.
And your latest (above) trivialities merely prove the fact that trivial 'proofs' are NO 'proofs' at all about the fundamentality of the entities involved. You on;y manipulate TRIVIALLY the exponents (as I already pointed out), and it's 'rules' were thus reduced to triviality. If that is your aim, then you trivially succeeded.
Asking "1-1=?" is trivial and doesn't make you 'smart', only 'trivial' minded and not interested in the fundamentality of the entities being used in such trivial manner.
And (my bolding) your " ...$$x^0=1$$ provided $$x$$ doesn't equal zero, for whatever reason." textbook exercise is CONDITIONAL from the outset, and hence not universally non-trivial UNLESS we identify what "0" is fundamentally BEFORE we use such trivial 'rules' based on 'exemptions' from the outset which make those 'rules' trivial and invalid for any truly fundamental 'proofs' to be derived from it.
Mate, seems like you are reverting back to the 'personal' source rather than the objective ideas presented which make your 'trivial' offerings moot insofar as any fundamental insights coming from your trivial (and nonsensical, according to Tach) offerings so far is concerned.
Try to rise above triviality and understand fairly, rather than again proceed to personally disparage and 'frame' from old baggage while you miss the fundamental thrust/insights involved. This site is more than just your 'social media' spot for posting trivial and personal garbage, B w/S. Learn from what happened to Tach when he kept bringing the site/discussions down to the malicious/personal level like that from ego and personal baggage.
Treat the science content fairly and try to understand something new which may be against your 'training/prejudices'. That is what this site encourages now, not that old time 'personal' stuff. Ok?
If you don't get it now, then you have missed it altogether. Good luck, mate!
A vacuous post with "trivial" used 18 times?
Vacuous? How do you know, since you obviously didn't read it? Obviously, since if you had, you would have seen where your 'triviality proofs' and 'nonsensical offerings' manipulations are shown to be deficient when addressing the thrust of the points I made...and so would not have made your vacuous post quoted above.
If you want 'social media' level/opportunities for your inane trivialities, then go to the sites which welcome your kind of shallow irrelevant antics, Bw/S.
Bye.
Oh, maybe you should learn how to communicate through writing then.
Would be a good idea if you intend to write a book, I think.
Would be a good idea if you intend to write a book, I think.
If you agree to learn to think non-trivially, then all will be well, since it all seems to boil down to your trivial condescending approach to reading/understanding before making your vacuous 'social media redolent' remarks like that above.
The important thing is: Do you understand the math/physics thrust, implications and point/suggestion made/discussed; or do you continue to prefer to play in the shallow end of your social-media corrupted faculties and be content with that trivial intellectual existence? Your choice, mate. Bye.
Well, you first have to construct a logical argument and not just pile on more baseless ones for the sake of obscurity.
Nah, I am simply pointing out your fringe ideas, as usual. I trust that you are learning (albeit slowly) that zero is indeed a number, right?
That was done already. You obviously missed it. And your offerings in reply were clearly shown to be trivial, especially your attempted 'offerings' which were shown to be nothing but nonsense (and seen as such even by Tach, of all people).
If you have no sensible genuine contributions to make to the science/math aspects/discussion in question, then I suggest you stop your vacuous posts in case you are banned for same if someone reports you. I have not done so. But others might. Good luck!
Unfortunately for you, Tach can follow a logical sequence of events, where you can't.
It's like I already said of your fumblings to try and make something fit -they wont. Yet you persist, is your ego that fragile?
It's like I already said of your fumblings to try and make something fit -they wont. Yet you persist, is your ego that fragile?
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