Wikipedia:Reference desk/Archives/Mathematics/2019 October 17

= October 17 =

Concept.
If you have

A = C, then we know, as A gets bigger and bigger, so does, C, and as A gets smaller, so does C.

And if you have (below as fractions).

A   C -  =  - B   D

Then as A gets bigger, so does C, and as A gets smaller, so does C. And as A gets bigger, B and D get smaller.

But what if you have.

A/B = C, and A = C/D, can you draw conclusions on "the bigger and bigger A gets, does C get bigger or smaller?" Or do mathematicians say not definable? 67.175.224.138 (talk) 08:48, 17 October 2019 (UTC).


 * Your statement regarding $$\frac{A}{B}=\frac{C}{D}$$ is incomplete (and in one case incorrect). Try:
 * As A gets bigger (grows larger in magnitude), and B and D remain constant, then C also gets bigger.
 * Similarly, as A gets bigger, and C and D remain constant, then B gets bigger.
 * And as A gets bigger, and B and C remain constant, then D gets smaller.
 * Regarding your question, C grows as A grows in both cases, assuming B (for the former case) and D (for the latter) remain constant. Otherwise is it not determined.  You can derive this from the first equation by setting one of the denominators to one.  (That is, set D=1 for the former case and B=1 for the latter.)-- ToE 14:25, 17 October 2019 (UTC)
 * ToE, you seem to miss the case of B and D being constant, but of opposite signs (as OP does), in which case as A gets bigger, C must get smaller. .. --CiaPan (talk) 17:50, 17 October 2019 (UTC)
 * My parenthetical remark "bigger (grows larger in magnitude)" was intended to apply to all uses of "bigger" and "smaller" -- that is, they grow or shrink in absolute magnitude. Perhaps I should have  been clearer, and also stated that those values which shrink in magnitude do not change sign, and that no values are zero.-- ToE 19:01, 17 October 2019 (UTC)
 * I recall seeing this concept discussed more in physics and chemistry classes than in math ones, and I thought it was referred to as arrow analysis (because it involves drawing various up and down arrows next to the variables of a formula), yet we don't have an article by that name and a Google search on the term doesn't yield any relevant links. So what is this concept properly called, and do we have an article on it? -- ToE 14:33, 17 October 2019 (UTC)
 * And if you have, $$\frac{Aa}{Bb}=\frac{Cc}{Dd}$$, then A = BbCc/Dda, a = BbCc/DdA, where's the point where it is undetermined if we don't know how many variables remain constant? All but 1 variable? For numerator or denominator only, or for both of them. (1 unknown in each, or 1 unknown altogether)? 67.175.224.138 (talk) 16:36, 17 October 2019 (UTC).
 * Yes, generally speaking, you need to know the behavior of all but one variable in a formula to know what the remaining one will do. (1 unknown altogether, because in many ways the numerator isn't much different than the denominator.  Division is just multiplication by an inverse.)
 * Note that you may be given the behavior of all but one variable and still not be able to predict what the remaining one will do. For instance, in your original $$\frac{A}{B}=\frac{C}{D}$$, if you are told that both A and B are getting  bigger while D remains constant, then you are unable to predict the behavior of C because A getting bigger would tend to make C grow while B getting bigger would tend to make C shrink, and you don't know which effect would dominate.  But if you were told that A was getting bigger and B was getting smaller, all while D remains constant, then you could predict that C will grow.  Does that make sense?
 * A question for you. Where are you running across this concept, and what is it generally called? -- ToE 19:14, 17 October 2019 (UTC)
 * I wouldn't know what it's called, the closest thing I guess is dimensional analysis, and this is taught a little in chem class when it comes to gas laws, PV = nRT, just trying to expand on it. I'm working on my own file on chemistry, physics, biology, computer science, and various other cross-topics. I'm recently thinking of working on a new document for concepts. I think a lot of the "concepts" in chemistry and physics are just pure math. If you take out all the math concepts in chemistry and physics, what's left? Then, once we find a non-math concept, we can list all the subjects that cover them. So recently going over biology and chemistry textbooks for that. For example, substitution is a concept used in organic chemistry as well as math. But eventually, I'm working on concepts used outside of math or science, like in human to human interactions. 67.175.224.138 (talk) 19:23, 17 October 2019 (UTC).

Other concepts
Here's an example of concepts found in several sciences: water travels from high concentration to low concentration, gases travel from high pressure to low pressure, and electricity travels from high voltage to low voltage. Can anyone think of a 4th? The 3rd 1 is the most abstract to me, voltage is ultimately another word for "pressure." This prolly falls under a concept of spontaneity. 67.175.224.138 (talk) 19:57, 17 October 2019 (UTC).
 * I just added the subheader to separate this from your other question. Hope you don't mind.
 * From your examples, I take issue with the specifics of #1 (if two solutions of different concentrations are separated by a semipermeable membrane, osmotic pressure will drive water flow from the solution of lower concentration to that of higher concentration -- though perhaps you were thinking of the concentration of water in the solution, not the concentration of solute) and #3 (in a circuit, electrons will flow from a point of more negative voltage to that of a more positive voltage -- though perhaps you were thinking of positive charge flow, which may be used to analyze circuity even when it is only the negative charges which are mobile), but I suspect that the general concept you are reaching for is scalar potential and its associated vector field, with the resulting motion of a test particle. For a fourth example, consider gravity potential. -- ToE 23:02, 17 October 2019 (UTC)


 * Agreed. Electricity travels from high negative charge (lots of free electrons) to low negative charge or even positive charge (missing electrons). For mechanical systems, there could be moving from high gravitational potential energy to low, like a rock rolling down a hill, or from some other form of high potential energy, like a wound watch spring, to low potential energy (unwound). SinisterLefty (talk) 02:26, 18 October 2019 (UTC)


 * So would more-negative voltage be high voltage, and more-positive voltage, be low voltage? And for the above, would lots of free elections, be high voltage, and missing electrons, be lower voltage? 67.175.224.138 (talk) 02:54, 18 October 2019 (UTC).


 * No, see electrical charge and electron hole. Voltage is the difference in charge between two points. Electrical current (amperage) is the rate at which charge is flowing. Electrical resistance (ohms) is a material's tendency to resist the flow of charge. SinisterLefty (talk) 03:27, 18 October 2019 (UTC)


 * If voltage is the difference in charge between 2 locations, then does "high voltage" and low voltage, mean anything in physics? 67.175.224.138 (talk) 03:32, 18 October 2019 (UTC).


 * Sure, it means more difference in charge (high voltage) or less difference in charge (low voltage). It is unusual that they have a word for it, though (voltage). There's no word for the difference in air pressure between two regions, for example. "Pressure differential" would be the closest term. SinisterLefty (talk) 03:36, 18 October 2019 (UTC)

Heat flows in the direction that will cause an increase in entropy. Dolphin ( t ) 03:31, 18 October 2019 (UTC)
 * Aside from that, doesn't heat travel from the hotter area to the cooler area, at about 90% of the time? 67.175.224.138 (talk) 03:42, 18 October 2019 (UTC).


 * I don't know about 90%, but unless something else (like an air conditioner) is forcing it the other way ("uphill"), yes. SinisterLefty (talk) 03:43, 18 October 2019 (UTC)


 * Air conditioner? I was talking about the micro- or quantum level. 67.175.224.138 (talk) 03:48, 18 October 2019 (UTC).


 * Then you may be interested in Maxwell's demon. SinisterLefty (talk) 04:13, 18 October 2019 (UTC)

Okay here's another concept, which is like a lack of imagination. I kind of categorize it "people who think like minimum wage employees and people who don't think like minimum wage employees." I walk into a Dunkin Donuts order a small hot chocolate. 3 cup sizes. When they out of small cups, a young female employee will use a medium cup, but not fill it all the way, say, ~80% full, but still charge it as a small cup. (Or if out of small and medium cups, use a large cup, but fill ~60% full). Then 1 day, with an old guy employee, they were out of small cups so he asks me to buy the medium cup instead, for X more cents. I said no thanks and takes off, and he still says to me "medium cup, only __ more cents." And he's someone who could have worked with Dunkin' for years, and still doesn't think of this idea. The interesting thing is, I tried sending an e-mail to corporate Dunkin' if there is a policy against this situation: if you're out of small cups, can you use a medium, but still charge it as a small cup, but not fill as much? I asked if there was a corporate policy, and so these employees are secretly not caring, or is this policy dependent on the individual store (up to the store manager). And they responded back avoiding the question. Sigh. 67.175.224.138 (talk) 03:52, 21 October 2019 (UTC).


 * I've tried to get places to give me a small amount in a large cup, so it won't spill. They rarely comply. I believe it has to do with the inflexibility of their system, causing their inventory of cups to not match what they expect. But none of this has anything to do with math, so it should be moved to the Misc Desk. (The previous part maybe to the Science Desk.) SinisterLefty (talk) 03:57, 21 October 2019 (UTC)