studiot

I learned Forth in the 1980s to get around just this problem.

Hey Clint, if you are feeling soppy tonight, perhaps you should start a nostalgia thread.

Sensei is correct. In the days when working memory was severely limited people prided themselves in how small ther program (now called app) was. Now nobody care how wasteful modern programming is. Just consider the plight of an IT department that tries to get someone to clear out their Email box. Sensei was also talking about machine code, and somebody has to write the interface code between the hardware and the software. Most 'programmers' find this the most difficult part to do. Yet hardware designers are accustomed to doing this as a matter of coursen with all sorts of electronics kit, from MigL's days to modern times.

Yes it depends how much the OP want to do for himself and what exactly is meant by an operating system. +1 for raising the subject.

You must first learn the connection between the instruction set of the microprocessor you are proposing to use and the physical 'pinout' of that microprocessor, unless your m/p comes with an inbuilt language, in which case you need to learn that, but you will still need the pinout. A microcomputer implementation has several blocks in its block diagram (Have you seen a block diagram). These involve the processor or CPU, input and output, storage, sensors and more. Please note that you have a maximum of 5 posts in your first 24 hours. You are now up to 4 so use the last one more wisely.

Sensei and I are both trying to guess what you want to talk about. The good news is that your subject (whatever it is) is Scientific (Mathematical), not another nonsense thread - we already get too many of those. I'm glad you have seen most of my functions before. That makes it easier to talk about. Yes they are from Real Analysis, except the ceiling and floor functions which are from Discrete or Concrete Analysis. Sensei is talking about Numerical Analysis, which is indeed a very important point. His 'control points' are those where some replacement function exactly matches the 'correct' function in value, curvature or some other property. We variously call the replacement function an approximating function, a test function, a collocating function, an interpolating function and so on. Numerical Analysis is about what happens between these points ie the difference between the test function and the correct or actual function. Some of this can be done with Real or Complex Analysis, some needs to be done with Discrete Analysis. But you haven't answered my questions about domains and co domains Or what you want to discuss about any of these functions, here in this thread.

Nothing to be sorry about. So as far as I can see we are not talking about 'control' points in curve fitting, but please correct me if I am mistaken. If you have x then your domain (do you understand what a domains and co-domains for functions ?) is a line we call the x axis. If you have x and f(x) then you have a plane. So sgn(x) divides the a axis line into 3 regions thus [math]\left\{ {{\mathop{\rm sgn}} \left( x \right) = \begin{array}{*{20}{c}} {1:x > 0} \\ {0:x = 0} \\ { - 1:x < 0} \\ \end{array}} \right\}[/math] and for the modulus of sgn(x) we have [math]\left\{ {\left| {{\mathop{\rm sgn}} \left( x \right)} \right| = \begin{array}{*{20}{c}} {1:x \ne 0} \\ {0:x = 0} \\ \end{array}} \right\}[/math] However the function [math]f\left( x \right) = \sqrt x [/math] is only valid for [math]x \ge 0[/math] There are also more modern functions called floor and ceiling functions we could discuss. Am I on the right lines and what did you want to say about such situations ?

Several thoughts. 1) A motherboard provides mechanical support and fixity as well as electrical connections for componenets, sockets, shields and smaller sub boards (daughter boards). 2) You need to do a search for makers or manufacturers of prototype (circuit) boards, in your area. Such companies make one off boards to order and you can discuss details with them. Some companies will also populate the board for you. Others just produce the bare board. 3) Circuit boards come in several different types, from the simple one sides with components on one side and tracks on the other, to to tracks on both sides and componenets on one or both sides to 'bonded sandwich' construction of several layers of board each with its own individual tracks. 4) Simpler boards use component leads soldered both sides, to provide electric continuity between one side and the other of a board. More complicated boards use what is called 'through plating' to provide this. Many componsnts no longer have leads and are so called SM or surface mount. Different fixing and slodering techniques apply here. 5) The method of soldering also comes into play especially in choosing the material to resist the heat of industrial solder bath methods. Does this help ?

It's not vague. It's actually quite clear and precise. It's just that you would never come out with a statement like that on its own. The Germans have an expression for what it is not Ist noch nicht selbsverstandlich.

Much as I hate to agree with John Cuthber, I have to in this case. The original statement is a very poor example that IMHO cannot be translated into formal logic. It is meaningless without the context that would remove the ambiguities John mentioned. English permits many forms of statement that are excluded from formal logic.

I'm sorry I can't make head nor tail of what you want to say here. Google doesn't produce anything relevent for specifically defined functions. https://www.google.co.uk/search?source=hp&ei=Y3CYX5qXH8ubjLsPnfG3yAI&q=+"specifically+defined+functions"+&oq=+"specifically+defined+functions"+&gs_lcp=CgZwc3ktYWIQA1DaDljaDmDkGGgAcAB4AIAB7gGIAe4BkgEDMi0xmAEAoAECoAEBqgEHZ3dzLXdpeg&sclient=psy-ab&ved=0ahUKEwja1KnHvNXsAhXLDWMBHZ34DSkQ4dUDCAg&uact=5 You seem to be talking about restricting the domain a function. Please re-organise your thoughts in your own language and have another go at saying what you mean in English. Do you realise that there are functions that cannot be written in terms of 'elementary' functions? Functions such as elliptic integrals.

I don't know if you like Science Fiction, but the novel by Poul Anderson might cheer you up . It has a positive ending or recycling. Tau Zero.

Yes indeed +1 Have you not heard of Einstein, Cavendish, Wordsworth, even Napoleon made a contribution to Mathematics. Whilst in more recent times most people involved in Science gained their livelyhood from it, in the past a significant majority did not. Some were of independent means (Cavendish), some had other jobs (Einstein) , some had other callings (Wordsworth) , some were elite supported by slaves (ancient Greeks) and so on.

So I have finally conquered the MathML here for tables. Here are the Cayley Tables I referred to earlier. [math]\begin{array}{*{20}{c}} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}[/math] So the rules are 0 + 0 = 0 0 + 1 = 1 + 0 = 1 1 + 1 = 1 These demonstrate the commutative and additive inverse requirements for both 1 and 0. [math]\begin{array}{*{20}{c}} X & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1 \\ \end{array}[/math] 0 X 0 = 0 0 X1 = 1 X 0 = 0 1 X 1 = 1 These demonstrate the commutative requirements for 1 and 0 and multiplicative inverse requiremtnts for 1 0 is not required to have a multiplicative inverse.

Trying to post a Cayley table [math]\begin{array}{*{20}{c}} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}[/math] [math]\begin{array} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}[/math] [math]\begin{array}{*{20}{c}} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}[/math]

It's that Thermopylae spirit.

Sometimes in English it is even worse since you need the pronunciation to understand the meaning. What do you think this means? I had a row with my boss at lunchtime.

Now that this thread has reached the wonderful anecdotal climax, many thanks I love it +1, surely the thread can be closed as a repeat of earlier nonsense.

I can see my table in the list in the activity tab, but I can't see it in the thread itself. This is even after refreshing the thread in the normal manner for MathML. [math]\begin{array}{*{20}{c}} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}[/math] [math]\left( {\begin{array}{*{20}{c}} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}} \right)[/math] [math]\begin{array} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}[/math] [math]\left( {\begin{array} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\ \end{array}} \right)[/math]

An excellent observation +1. There is one mitigating factor to this however. Submarines are not subject to such severe weight constraints as aircraft so the addition of the necessary strengthening bulkheads is far easier.

[math]\begin{array} + & 0 & 1 \\ 0 & 0 & 1 \\ 1 & 1 & 1 \\\end{array}[/math]

Read Here https://en.wikipedia.org/wiki/GF(2)

I agree that the OP proposition does not constitute a field, since it does not contain the required inverses. However the smallest field contains just two elements, along with appropriate rules for addition and multiplication. An example would be {1, 0} with a De Morgan/Cayley table.

Thank you for sharing your experiences. We are seeing the resurgence partly because too many folks are not taking it seriously enough. Also partly because too many prominent folks are setting bad examples.

I would suggest to try to concentrate on the here and now. The philosophy of living for the moment (also called mindfullness apparently : ref google). This technique has helped many people.