studiot

What do you mean by a string ? What is it made of ? Where did it come from ? What are its properties particularly in connection to time ? What is its connection to positive and negative ?

I have also found an electrochemical procedure for determining sulphite (added commercially as a preservative) in white wine, if you are interested. Note what exchemist and my attachments said about there being other acids so a pH meter will not directly compare with what appears to be an industry standard using only tartaric acid. Perhaps industry now has an ion selective electrode for tartrate.

Here is a procedure for determining the acid content of a wine

titrating for ppt ? Can you elaborate on this ppt only means power point to me. I know little of winemaking chemistry, but understand that various measurements can be made as well as acidity. The fruit contains sugars and fruit acids to start with. These are fermented first to alcohols and then to vinegars by the action of the yeasts. So chemical monitoring is more complicated than just measuring acidity.

Yes, different and completely imaginary story. Not interested. I seem to have completely misunderstood you intentions. I thought this was about the use of mathematical theory in Physics, which is why it was posted in the Phyiscs section. Your last answer seems to imply that it is nothing to do with physics at all ??

I recommend this book edited by Shahn Majid - Cambridege University Press It is dedicated to the issue of granularity v continuity in real physical space. Please note that a mathematical space is quite a different animal.

Well If I knew what yoy might not have fully understood, I might be able to help. The podcast was overlong and oversensationalist for my taste but they did make a clear distinction between imaginary and complex numbers. They also pointed out that 'imaginary' is a bit of a misnomer as imaginary numbers are every bit as rigorous and valid as real numbers. The thing is that the terms imaginary, virtual, borrow 1, are just examples of a technique used in both maths and science more generally. Children become comfortable with the idea of 'subtract 19 from 435' by saying 9 from 5 wont go so add (or borrow) 1 (when they really mean add 10), now 9 from 15 leaves 6 then add 1 back to the 1 from the 19 or take it off the 3 in the 435 to get the answer 416. A more advanced version of this is solution by substitution of variables, both in algebraic and differential equations. Engineers and physicists have long used virtual work, virtual displacements, as powerful tools for solving classical problems and more recently we have the virtual quantum paticle. The podcast also floated the idea that all these things are devices to help solve equations by the perhaps perhaps permanent temporary introduction of something new. Centuries after the controvery of imaginary numbers a similar difficulty arose describing angles and rotations in higher dimensions. This was eventually resolved (Hamilton) by the introduction of dyadics, quaternions and octonions. But none of these are directly involved with the op question of (my paraphrasing) "Why do we bother with the reals when the rationals are nearly as good" ?

Good morning. I am in two minds as to whether to bother with this thread, given your opening preconditions. My first reaction was Where is the Physics in all this ? However your actual question is more reasonable. So perhaps you might like to replace that opening leg-iron with some useful context. For instance, at what level ae you seeking this system ? Sub-atomic particle level. Or macroscopic atomic physics and above? Although there is some small ovelap, fundamental units in these realms are mostly quite different. For instance you mentioned the Ampere, which has no meaning at sub atomic level. Further when you say units, how are you relating these to the well described 'method of dimensions', used throughout science and engineering ?

I don't know about any podcast, but my answer to your question is a simple no it is not. By the way are you (and they) confusing imaginary numbers with complex numbers ?

Don't worry, meaning is not a defined mathematical term. It is really a language/ philosophical thing which requires interpretation which in turn requires context. Mathematics and logic, although different, are about 'statements' and their consistency in the case of mathematics and validity in the case of logic, although there is obviously some overlap. Would the statement "lines are green" add anything to the 5 axioms of Euclid ? I haven't time at the moment, but I will try to address your other question later.

Thanks. Intuition is the right word. Continuity and infinity are strange beasts. The thing is that in Physics we can shift the coordinate system any distance we like, including by a single point. This implies that in performing that shift we can overlay a rational point with an irrational one and vice versa - something we cannot do in maths.

The point is that in order to draw a continuous line your pen must pass through irrational points to get from one rational to the next. Equally for (physics) fields to follow the equations of physics, the field lines must pass through irrational points to get from one rational point to another and in order to make a completely closed line or shell or surface or whatever a the closure must block the flux from escaping through irrational points on that closure.

No. Does 4 implies 2 have any meaning? Yet 4 is related to 2 and in this case 2 is related to 4 since they are both even. Further this relation can be transferred so if 4 is related to 6 and 2 is related to 4 then 2 is related to 6. The three statements a R a is called reflexive relation a R b implies b R a is called symmetric relation If a R b and b R c then implies a R c this is called a transitive relation. Relations may satisfy none, one or two or three of these conditions If the last three are satisfied then the relation is called an equivalence relation and often given the symbol a ~ b Equality is an equivalence relation, but > is not since a > b does not imply b > a.

It is worth noting that there is some disparity in drawing the distinction between a relation and a function and considerable disparity in the notation employed. So it is always wise to check the definitions and notations used in any particular work. Here is simple explanation of how I like to think of relations Given a set A we often like show that a 'relation' exists between certain pairs of the elements of A. Such a relation can be expressed as a property statement that is true for some pairs of elements but false for other pairs. A good notation that does not clash with other uses (such as the ~ symbols which may be reserved for a special type of relation) is For all a, b in A a R b denotes that b is related to a c notR d denotes that d is not related to c A relation property may take many forms. For instance a is related to b if they have the same parity so all even numbers and all odd numbers are parity related. (This is a relation that is not connected to a function) Another relation that is not is function is the equation of a circle in a plane. That is because there are two values of y for every value of x and functions are defined as being single valued. This is the principle distinction between a function and a relation.

What do you mean by this ?

Hippasus already gave you one. Remember the ancient greeks were primarily geometers, not algebraicists. But not only geometers but constructive geometers. Note that most of Euclid is couched in terms like Proposition XXX To construct ........ So imagine their consternation when they discovered that they could not measure the length of that diagonal, although they could undoubtedly construct it.

jesus math is old. Was not aware of this fact. Thanks for this. To be fair what he showed was "There is no set of all sets" ie no Capo di Capo", no "One ring to rule them all. It is perfectly OK to posit a simpler universal set which is the complement of some set plus that set itself. I agree with the others that I saw no sense in your use of an arrow though. Nor do I understand your definition of a relation, which can be thought of as a partition of a set.

Of course it would. The diagonal of a unit square would be different for instance. I'm not sure if the triangle inequality or Schwartz inequality which underlie quantum theory would also be different.

Don't see why you need to get all fancied up; Hilbert space ? What is wrong with good old fashioned Hippasus ' square root of 2 ? Or Archimedes and his Pi ?

So how am I meant to take this ? You don't know anything about neighbourhoods but you don't want to consider them ? Why not ? Why is this not inconsiderate of others who are trying to help you ? As far as I can see you are having trouble reconciling the concept of infinity and infinite processes with your half completed half remembered past studies. Further you keep intorducing infinity and things which are not numbers or even necessarily to do with numbers. As soon as you start talking about integrals you have left the realm of numbers - real or otherwise - and entered the realm of functions. Functions are not numbers and numbers are not functions. In fact the Riemann integral is a mapping from the space of functions to the space of numbers (please note the correct use of the word space here) Not only that it is a linear mapping called a functional. Be that as it may here is one way in which neighbourhoods help avoid infinity. There are different types of neighbourhood defined. A simple neighbourhood of a general point p which includes the point p itself and a reduced neighbourhod of p which does not include the point p itself. By using the latter we may avoid infinity if we define a reduced neighbourhood of p as ∞ as being {x: x > c} where C is some chosen number. Do you understand this notation ? It means the set of all numbers greater than some C. The implications of this are huge. It means that it does nor matter whether there is an infinity or not - we only have to 'approach it' or 'tend to it'. Equally useful mileage can be obtained from the reduced neighbourhood of a real number point p, since it must include any 'nearest real number' - if such a thing exists. But we can still proceesd with out analysis if it does not. Also, and back to integrations and functions, we can use neighbourhoods directly with functions. We cannot so use the other derivations without modification. What's not to like ? Here is a link to a good article about intervals and neighbouthoods. Note they use 'a' for the point, p where i have use 'p'. https://math.fel.cvut.cz/en/mt/txtb/1/txe3ba1a.htm

Just type create recovery usb into the search box nxt to the windows button in the bottom left and follow the instructions that open up. You can see the screens you get in my links. Windows will work out how big the usb stick needs to be, it will probably be in the range of 8Gb to 16GB. Let Windows make the stick and put it away safely. Once a month or two or so update it and changes including udates and apps will be automatically included. When in trouble The stick will boot the pc and offer recover, repair, restore and all the other words in your list.

Don't forget that from W10 windows creates a required hidden partition on your hard drive, partly as a security measure. Simply copying the win partition will no longer work. Also many machines these days have machine specific and drive specific signature codes that must be correct.

OK so you are a dreamer shooting the breeze. Nothing wrong with that since you are asking for advice. Firstly gravity. Earth's gravity depends upon the mass of the Earth, not its orbit. So unless the meteor combined with Earth (as Phi said) and it was a mighty big one gravity would not have altered. BUT The idea of something altering is not so far off. You also mentioned the dinosaurs. Yes they were big. So were the plants in those times. W know from paleoclimatic data that the average temperatures were higher and there was much more of both oxygen and carbon dioxide about in those days. Here is a quote from professor Beerling (Sheffield) in The Emerald Planet - Oxford University Press So don't give up on having ideas, you may be right next time.

More or less yes, but you need both it is not a question of versus. Also sometimes fundamental principles are enough. Most times they are not. As for example in the phrase 'statically determinate' In two dimensions there are three fundamental equations available. After that you must introuduce others somehow if they are not enough - which is mostly true in real life.

You clearly don't want to understand since I offered you an alternative treatment using neighbourhoods and you ignored it totally. The beauty of neighbourhoods is that it does not depend upon whether or not there is a smallest real number or a nearest real number or what happens at infinity. And yet neigherbourhood analysis arrives at the same results as the other approaches you have been arguing about.