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My very short answer: A value of a random variable. Let's say you receive a symbol "1". If this is the only possible symbol the fact that you received it does not give you information. But if this symbol is one of two possible, "0" and "1", then the reception of symbol "1" may contain information. So having more that one symbol is a requirement, but not sufficient. Lets say you receive the pattern "111111...". The probability of the symbol "1" is 1. Again there is no information. But if random sequences are allowed, for example "00", "01", "10", "11" then we may use these sequences to represent information. So conceptually information can be seen as a value form of a random variable. The above is an attempt at an extremely short introduction to information theory, which is tied to discrete probability theory. Most important early contributor was Claude E. Shannon and his paper “A Mathematical Theory of Communication”, dealing quantitatively with the concept of “information”. Shannons concepts and the mathematics he used to describe information and to measure information content is a remarkable contribution. I believe it's tricky to find any areas of IT where his work does not contribute. Wikipedia* has links to some concepts related to your question. Feel free to ask additional questions. *) https://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication For an early predecessor of Shannon, working on sinus signals and frequencies, see Hartley: https://en.wikipedia.org/wiki/Ralph_Hartley

I want this thread to be an attempt to create a generalized overall mapping of mathematics as we know it at this current time. Its basis is that all models developed by a human is itself a model, therefore I do not want to delve to deeply into the philosophy of the subject matter, whereas I would like for this to be an overall model of existing mathematics from beginner to expert levels all explained and viewed as a general "mapping." Showing the interconnections between all of the different mathematical concepts formed which have been agreed upon. Showing all the twists and turns, all the connections, all of the branches that lead to no where. This is a big project, I am not blind to that. However I believe that providing an overall visual mapping of mathematics as a whole will allow for a sort of "key" for future persons, a minute or a millennia away, to quickly and easily view the processes that exist so that they themselves can go back and see the holes in their knowledge. While also quite possibly coming up with new ideas and adding to the overall mapping of the analogous "cinematics math's universe." The goal of this project is for anyone, anywhere, at anytime to be able to learn all of mathematics in a minute. To be able to master it and contribute to it in a matter of moments. I would also like for this to grow into something more, one in which instead of conceptualizing the concept of mathematics and guessing what exists based on a developed mental mapping, there is one that actually exists. Where you can add your own name to. Like a gigantic tree of knowledge or something. Thank you for your time

Thank you for your help and advice. My sister opened her eyes today and acknowledged our presence.

When I was younger (the 1960s) I used to look forward to the Analog Science Fiction Annual every year. One year there was a short story called "Business as Usual During Alterations" Essentially some Aliens dropped a matter duplicator onto theEarth. At first everyone thought that would be the end of 'commerce and work and MONEY' But then some enterprising souls got a duplicator and started offering the service to "Duplicate your stuff for you to your requirements" And the good old American Dream was saved.

I remember when I was very young thinking about this. Suppose we just let people go into a store and TAKE whatever they want! Since everyone can have whatever they want, no one would complain. Then as I got older I discovered a very important, very disturbing fact- work is hard! Most people would not want to work if they did not have to have money! What if we could just go into a store and take whatever we want, but discovered that there was not anything in the store? Who would plant, grow, and harvest the vegetables? That's hard work! If farmers did not need the money they wouldn't do it! If tailor's did not need the money they wouldn't make shirts, slacks, suits!

I echo SJ's notion of finding another medical specialist. IIRC Citrobacter are often found in urinary tract infections and the prostate in turn is vulnerable to UTI. Also note that often the boundaries between pathogens and non-pathogens are fluid. If normally non-pathogenic bacteria get into areas they shouldn't or number that are too high, they still can inflammation and other issues.

Should really consult a doctor or nurse about this(over the phone if necessary). Just as an example, there is DPD deficiency. Where a lack of the enzyme can impact how quickly your body is able to break down some chemotherapy drugs. https://www.cancerresearchuk.org/about-cancer/cancer-in-general/treatment/chemotherapy/side-effects/dpd-deficiency Good luck and I hope your sister recovers.

Not sure I grasp the idea completely but maybe the "the map of mathematics" could act as a starting point or act as a rough guide? It is a one page drawing showing how many concepts such as pure mathematics, applied mathematics, number systems, topology and many other fits together: https://www.flickr.com/photos/95869671@N08/32264483720

Quite a bit is pretty fanciful from a scientific perspective, but is an extremely well done production. The setting is a fair sized city set inside of a large martian dome. Heavily modified assets and ridiculous level of detail really make the city come to life. The actual build aspects may not be everyone's cup of tea, but I've found it easy enough to skip past when things become too dry.

First time interacting with dimreepr, eh?

It's normal in the intestinal tract. Maybe somebody else will chime in.

Just about every major pursuit is going to provide employment, but few investments give the kind of global returns that space exploration and other scientific endeavors do. The amount of new knowledge produced is fairly staggering, every time we take the risks to expand our knowledge and banish our ignorance.

The shortest distance between a point and a line (which is what is meant by "the" distance between them) is along a line perpendicular to the line. The line is given by y= 6x+ 3 so has slope 6. A line perpendicular to that has slope -1/6. The line through (6, 2) with slope -1/6 is y= (-1/6)(x- 6)+ 2 so 6y= -x+ 6+ 12 or x+ 6y= 18 Substitute (two lines which intersect) y=6x+3 into x+6y=18 and you get: x + 6(6x+3) = 18. x + 36x +18 = 18 37x +18 =18 37x = 0 x = 0 So that means that x=0 at the point where the lines y=6x+3 into x+6y=18 intersect. Substitute y = 6x + 3 y = 6(0) + 3 = 3 y = 3 The point of intersection is (0, 3). Then, use the distance formula to find the exact distance between (0,3) and 6,2) d^2 = (x2 - x1)^2 + (y2 - y1)^2 So the distance between (0, 3) and (6, 2), squared, D^2= (0- 6)^2+ (3- 2)^2= 37 and then D= square root (37).