studiot

Your own Bible gives the lie to that statement. Seems to me a pretty clear record of antisocial behaviour by the leaders gangsters? of the day. So you do want to tell a Mathematician what an equality is. Wow and goodbye.

Is this another attempt to bash mass production ? Suppose you wanted (to build) a house. Would you make all the bricks individually one at a time or would you think mass production might be advantageous ? Furthermore would you follow the brickmaking instructions in your Bible when you made them ?

Please don't try to tell a Mathematicain what a mathematical theorem or its proof is. Probably the most famous counterexample (do you know and understand this word ?) is "The triangle inequality" which is, by definition, not an equality and was known before Euclid. FYI there are many uses of such mathematical structures in Physcs, for instance the Second Law and The Uncertainty Principle.

Well to continue the themed answer. The OP asked about surfaces, and I was trying to put things into context. I have chosen the plane and hyperplane because their geometries are linear. The plane and hyperplane are perhaps the simplest surfaces. We can build shapes in n dimensions considering intersections of lines, and planes. So we have polygons in 2 dimensions, polyhedrons in three dimensions and n-polytopes in n dimensions. Polygons are constructed from lines of (n-1) ie 1 dimension, but exist in 2 dimensions. Polyhedrons are solid shapes with surfaces constructed from planes. Again (n-1) ie 2 dimensions, but existing is 3 dimensions. Polytopes are shapes whose surfaces are (n-1) flats, existing in n dimensions so a polyhedron is also a 3-tope with 2-flat surfaces. Having got this far we can generate geometry on these surfaces and hypersurfaces. This will be the familiar Euclidian Geometry, or Cartesian Geometry if we involve coordinates. So for instance triangles will have interior angles adding to 180 and areas equal to 1/2 base times height, that will not vary with position on the surface. When we come to curved surfaces equivalent triangles will not be so simple to handle. Also we can generalise polytopes to curved closed surfaces such as spheres and ellipsoids and more and even to more complicated object we call manifolds.

All agreed, but John, I'm disappointed, you didn't tell Bartholomew Jones (why do you have to have such a long name to write out ? ) about the Scottish verdict. In point of fact there are three increasing levels of proof required in an English prosecution ( and a different one for civil matters called the balance of probabilities). The Police require the lowest level of evidence to charge someone The Crown Prosecution service requires a higher level to take the case to court reflecting the likelyhood of a successful prosecution. The Court requires the ultimate beyond reasonable doubt for a guilty verdict. It is customary here for someone (usually Strange) to post the cartoon about peer review. I'm going to say +1 for being (I hope as well as appearing) open minded enough to ask a sensible question. In fact proof was not mentioned in you question. To proceed is not synonymous with to prove. In technical terms 'Theory' may include several 'Principles', which are the scientific equivalent of mathematical proofs. An axiom or principle is a statement offered without proof but in the knowledge that it is not known to be contradicted within the conditions of application. All too often the conditions part are forgotten, particularly in arguments (of the disagreement type). I have a great deal of sympathy with the point of view emboldened. For instance shoe manufacturers (or is it shoe retailers?) have stopped offering half sizes - which is very difficult for me as I am a half size. Definitely a retrograde development. Other clothing retailers do the same thing with other garments. But my point to you is that, once again your approach is an all-or-nothing (binary) approach to something which has a scale from good to bad or black to white with many many shades of grey in between. It is therefore possible to proceed too far in either direction away from a comfortable middle way. And the greed of some humans feasts on this to the detriment of all others.

What all 20 ? What subject are you studying that you do not know the answers to any of them ? How about your thoughts on question 17 ? Did you really not understand it ? This is simply a matter of common sense, although it contains some points of chemistry worth discussing I see that HOI and Chenbeier have done question 1 to death, it really is a chemistry question. +1 apiece.

Gosh you have got a lot of geometry and topology into this question. So there is a huge amount of terminology to master. Starting with the sequence of linear (= flat) objects point, line , plane, hyperplane ....... subsequent flat objects are also called hyperplanes or n dimensions or n-flats. point, zero dimensions line, one dimension plane, two dimensions hyperplane three dimensions, for more we do not distinguish further names just an n dimensional hyperplane. We can follow David Hilbert and build flat or Euclidian geometries of n dimensions using these. One of these objects of n dimensions divides or separates a space of (n+1) dimensions into two regions, both of (n+1) dimensions. So a point is a 0 dimension object that divides a line into two lines A line is a 1 dimensional object that divides a plane into two half planes A plane is a two dimensional object that divides 3 space into two regions (region is a respectable word for a subdivision of a space of any dimension) So the n dimensional object forms a boundary between the regions. Curved objects come later and involve more concepts and terminology, depending onif your interest is geometry or topology.

That's a heftly 7 inch lump of 1 inch rebar you have shown. It doesn't look stainless, which would offer good resistance to hydrochloric or sulphuric acids. But stainless rebar can look dull like that. It is not higly polished like cutlery. It looks more like standard high tenisle steel with the normal black oxide coating. The black oxide is what give cast iron its high corrosion resistance. You would have to expose clean metal to get the solution going. Even then, if it is a high silicon steel it might still be resistant. Why do you need to dissolve such a large amount ? Would some shavings not do ?

Flu vaccination in th UK starts in September and only the stragglers (like me) are left until December. I got mine in early this year at the end of November. I never notice any change after the vaccination , but my wife always feels 'off colour' for a few days and needs at least some paracetamol. We both still do it though since neither of us has had the infection for years. I'm equally sure it would be wrong to pretend that there will not be a range of reactions to the covid vaccine and that many will notice some mild effects. Absolutely sure this this far outweighed by the benfits like a ton to an ounce. As to whether the Pfizer vaccine is dead virus or fragments of virus is a bit of a pointless argument. If I gut and fillet a dead fish for the table, it is still a dead fish (but with bits missing). If I hold a hog roast the thing turing on the spit over the firepit in the garden is still a dead pig (but with bits missing). But if I put a loin joint of pork in the oven, that is fragment of pig. I understand the difference between the Pfizer and Oxford vaccines are the difference between my fish or hog roast and sticking the legs off a pig onto a turkey.

There have been more than 2 in the UK alone, and these were for the dose 1 stage only as no dose 2 stages doses have yet been dispensed. However the incidence and range of reaction is incredibly low compared to that of the normal annual flu vaccination. I can't speak for anywhere else as I have no information there. Possibly those in Scotland were not as severe, certainly no one has failed to recover from them.

Vaccination hasn't reached us lowly peasants yet, so this is the best I can do. https://www.bbc.co.uk/news/entertainment-arts-55315802

It is known that the covid virus affects people in a variety of ways and to a large range of severity. Experts are now beginning to uncover the genetics behind these differences. So one might reasonably expect there to be a corresponding range of 'protection' life given by the vaccine. The vaccines themselves (ther are several types) work in different ways as well. The Pfizer vaccine is basically dead virus. The Asta-Zeneca vaccine is basically a different virus with bits from covid tacked on. The reason for the original lower effectiveness of the Asta vaccine is thought to be because the first dose, if too stron, prepares to body to reject the carrier virus and never gets round to responding to the added covid.

Just to clear something up. The number itself is the same whatever "base" you use to represent it. It is the representation in each different base that will be different. It is often proposed that primitive Man started off with base 10 because he had 10 fingers and counted on them. This proposal actually runs counter to archeological evidence which suggests that different primitive Men tried different base systems in different places and finally more sophisticated Man settled on the 10 base because he had 10 fingers and still counted on them. Also you have introduced physical units; these are quite separate from the numbers themselves. The volume of my glass of beer is the same whether I measure in in pints, litres, quarts, hogsheads or US gallons. But the number representation in each unit system. This is perhaps where you should be thinking twice.

First you need to know that 0 and 1 are fractions themselves ! [math]0 = \frac{0}{1}\quad and\quad 1 = \frac{1}{1}[/math] Although we don't usually write them like that. Mathematics recognises a series of 'number systems' that are nested like Russian dolls. The outer one is the most complicated and the number systems get simpler inside just as the outer doll is the biggest and the dolls get smaller inside. For number systems the more complicated (outer) system contains or includes all the simpler systems within it. The simplest system is called the natural numbers or counting numbers. 1,2,3,4,5...... There is no zero in these. Then we have the positive inetgers if we want the same thing but with a zero 0,1,2,3,4,5...... The we have both positive and negative integers ...-5,-4,-3,-2,-1,0,1,2,3,4,5...... These are all the integers. The we have the rational numbers : ratios of two integers ie fractions [math]\frac{1}{2},\frac{{25}}{{39}}etc[/math] We do not need another category for the ratios of decimal numbers since they can always be written as the ratio of two integers [math]\frac{{2.5}}{{3.138}}is\;the\;same\;as\frac{{2500}}{{3138}}[/math] Which is a number system as far as you have asked since it includes all the fractions lying between 0 and 1 that can be written. And it also answers you question about number bases. Simply it does not matter which base you choose as shown by the example of rewriting a decimal fraction as the ratio of two integers. But there are yet more important numbers that cannot be written this way. An example would be the reciprocal of the square root of 2, or the square root of 0.5. So we come to the what are called the real numbers as corresponding to our outer Russian doll, and includes all these numbers as well as all the fractional ones. I hope you can see nesting idea from this. There are yet more complicated layers of 'numbers' but I will leave it at that.

Two interesting devlopments today. 1) Trials of a combination/cocktail of the Astra - Zeneca (Oxford) and Russian (Sputnik) vaccines are to be held. https://www.bbc.co.uk/news/health-55273907 2) Progress on the gnetic basis for severity of covid infections. https://www.bbc.co.uk/news/health-54832563 Finally an interesting story of a Cholera vaccine pioneer https://www.bbc.co.uk/news/world-asia-india-55050012

So does this mean anything to you, if so what ? [math]aBaC{l_2}_{\left( {aq} \right)} + b{K_2}S{O_4}_{\left( {aq} \right)} \to nBaS{O_4} \downarrow + mKC{l_{\left( {aq} \right)}}[/math]

Since you couldn't solve them you have presumably tried ? So how far have you got ? Have you for instance got any proposed reaction equations ?

Why straightforward ? In my opinion the headline question is pretty shallow since it assumes a binary choice of answers. Real life is not like that. What about those individuals who chose to sacrifice themselves to save others in all sorts of circumstances ? What about Kamikaze pilots ? What about the Hari Kiri of Japanese Officers ? What about those who were forced into it for whatever reason ? What about Hitler, did he jump or was he pushed and was his demise a good thing or a bad one ?

Just think of those folks who 'sailed for South Australia' in the late 18th and 19th centuries. Having spent some Christmasses offshore in the oilfieds and had later Christmasses dictated by the the needs of our local district hospital here, I don't have huge sympathies for those 'who must have their Christmas' just so!

Well thank you, I'm flattered as I don't deserve such special reatment. Anyway, You too have a good holiday but above all, Stay Safe. Too many in the UK are currently putting their 'right to a good hioliday' above the safety of themselves. This is their choice and perhaps their right but the trouble is that all rights come with responsibilities and they are also affecting the safety of other people by doing this.

Thank you. Thank you also for providing an accurate statement of the setup in Scotland we can all agree. So can I ask you to consider the value of accuracy in discussion ? Rather than going over old ground any more can we also discuss your title question ? Only the first line provides a discussion topic, I would rather not comment on the rest except to ask you to you consider if this is a good way to address people and open a conversation you hope to have an adult discussion with. So did you wish to discuss barriers to equal opportunity in 'education'. - as you state in the title or barriers to equal opportunity in 'academia' - as you state in your opening post ? I hope you are not conflating the two. They are not the same. In any event we need an agreed working definition of 'education' and 'academia' before progress can be made.

One point at a time. Initially I granted you the opportunity to expand on your statement in my short reply You replied And I offered this which is true. And you replied specifically zero costs, repeating your earlier contention. Currently the cost of a single Pharmacy textbook is in the range £35 - £75. A Pharmacy student wanting to have their own BNF (renewable every year) could fork out £400 A suitable laptop would cost in the range £500 - £600 Then of course there are living costs. And travel costs Not counting the opportunity cost of cost earned income during the time of studying. Now do you still maintain the zero cost option ?

Well if you must come here and promote complete and utter falsehoods, You introduced Scottish education, and I haven't yet finished discussing it with you or the falsehood you promoted about it. I tried to discuss the French, German, Dutch and Belgian systems but received no response whatsoever. First time I think perhaps I put too many points into one post so I have tried to cut it down to one point at a time. And you respond with a slap with a wet fish. I can't respond to these as I don't know what they are.

Your response here indicates that I did not manage to communicate my point. Sorry. I am not saying it is an either - or situation. I am saying that there is a scale between opportunity and result and the question of where a particular activity or situation falls on that scale is a question of ethics that can be discussed scientifically, particularly in the context of education, as required in this thread. Here are some examples from real life. Consider a runing race. 1) If everyone has the opportunity to run then they will not all reach the finish line at the same time, because they do not all possess the same ability or luck. 'Affirmative action' has lead some educationalists to ban races in some schools and try to ban exams. Where do you draw the line here and why ? 2) I have zero or even less than zero talent fo music, no matter how much musical education I am offered or receive. There are a limited number of stradivarius (and similar) violins in this world. Should I therfore be offered the opportunity to play such an instrument, therby depriving another player the opportunity or maybe breaking one ? Should I waste the time of the few people in this world capable of teaching the high standard necessary to obtain the best from such an instrument ? 3) Would you get into a taxi driven by a blind taxi driver, or should taxi drivers be drawn only from the ranks of well sighted persons? If so how well sighted ?

Education structures in Scotland have never been the same as in England. Holyrood was established on 12 May 1999. So it has been barely two decades. It is all too easy to expand and generalise to support a view, but this is Science site and we are supposed to discuss the subject in a scientific manner, not an expansive one. I am not clear if you are saying you attended school in Scotland, but surely you would know that it is disingenuous to suggest that degrees of any sort incur zero cost in Scotland. Some folks (mostly Scots) have their fees paid. This also used to be the case in England until greedy bursers and governments made them amongst the most expensive in the world. FYI, the structures in France, Germany, Belgium and the Netherlands, are hugely different, both from each other and from those in the UK. Edit I think you are asking the wrong question here. Consider this Which do you prefer equality of opportunity or equality of result ? You cannot have both, but you can make some adjustment to the balance between them. How to achieve a fair balance is the ethical dimemma.