# What is Comparison: Definition and 388 Discussions

Comparison or comparing is the act of evaluating two or more things by determining the relevant, comparable characteristics of each thing, and then determining which characteristics of each are similar to the other, which are different, and to what degree. Where characteristics are different, the differences may then be evaluated to determine which thing is best suited for a particular purpose. The description of similarities and differences found between the two things is also called a comparison. Comparison can take many distinct forms, varying by field:

To compare is to bring two or more things together (physically or in contemplation) and to examine them systematically, identifying similarities and differences among them. Comparison has a different meaning within each framework of study. Any exploration of the similarities or differences of two or more units is a comparison. In the most limited sense, it consists of comparing two units isolated from each other.
To compare things, they must have characteristics that are similar enough in relevant ways to merit comparison. If two things are too different to compare in a useful way, an attempt to compare them is colloquially referred to in English as "comparing apples and oranges." Comparison is widely used in society, in science and in the arts.

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1. ### A Parton distribution functions

Hello I plotted the Parton distribution functions in Mathematica. Now I want to compare the graphs drawn with the graphs of other groups(xu and xd). How should I do this?
2. ### Potassium Bichromate/Dichromate

Hello All I have a reference in a 1930s journal to potassium bichromate. Is this the same as potassium dichromate K2Cr2O7 ? ie dichromate is the modern terminaology to use. Searching on the www almost always finds the dichromate when I search for the bichromate, but maybe this is just the...
3. ### Is it possible to find a number x such that 5 < x < 1?

I don't think it is possible, but can someone please explain why? Many thanks!
4. ### Computational, Theoretical, and Experimental Research: A Comparison

Hi, I understand there is computational research as well as completely theoretical research compared to experimental research. I was curious about what they are like. Could anyone point out some good papers? Thanks.
5. ### I Comparison of Deur's universe vs. L-CDM

https://arxiv.org/pdf/1709.02481.pdf "Calculations have shown that field selfinteraction increases the binding of matter inside massive systems, which may account for galaxy and cluster dynamics without invoking dark matter. In turn, energy conservation dictates that the increased binding must...
6. ### Velocity comparison -- Which thrown mass hits the ground first?

On the test, I said they hit the ground simultaneously. However, that, in retrospect, doesn't seem to be the correct solution.
7. ### Photovoltaic vs. thermal radiator Solar Panel comparison (using a lens)

Hi, Has anyone experience with photovoltaic solar panels and thermal radiator type solar panels? 1/ How do they compare when both have the same collection area? If the thermal radiator was much smaller than the collection area, and a lens the size of the collection area was used, focused on...
8. ### Researching Turboprops: Fuel Comparison of Hydrogen, Methanol, & Jet A1

Hello I'm trying to get some good reference material so I can do a literature review on Turboprops and a comparison of PSFC of Hydrogen/Methanol/Jet A1 fuels for turboprops. If anyone knows any good source material for this please let me know as I have struggled to find anything. Regards, Michael
9. ### Image comparison software (similarity and differences)

Images comparison What are the best softwares available for comparing two images having similarity and differences? Two photos each of Margaret and Enid. 1 Margaret's first photo with her second photo comparison. 2 Enid's first photo with her second photo comparision. 3 Margaret's first...
10. ### Prove limit comparison test for Integrals

Attempt: Note we must have that ## f>0 ## and ## g>0 ## from some place or ## f<0 ## and ## g<0 ## from some place or ## g ,f ## have the same sign in ## [ 1, +\infty) ##. Otherwise, we'd have that there are infinitely many ##x's ## where ##g,f ## differ and sign so we can chose a...
11. ### Using comparison tests and limit comparison test

The answer sheet states that the series converges by limit comparison test (the second way). In the case of this particular problem, would it be also okay to use the comparison test, as shown above? (The first way) Thank you!
12. ### Parent/Child Genome Comparison: 100,000 Years Ago

Let's say you know you are given the full genome of 2 individuals such that they are related as father/son or mother/daughter, that they both died at age 30 some 100 k years ago. Can you tell who is the parent/child by looking at their genomes only? If so, how? I picked 100 k years only because...
13. ### Vaporization Heat and the Heat Capacity of H20 comparison

According to the Vaporization Heat table, the heat needed for 1 mol of H2O to evaporate at 100°C is 40.7KJ and 44.0KJ/mol is needed to evaporate H2O at 25°C. Thus 44.0-40.7=3.7KJ is the energy needed to heat H2O to 100°C from 25°C. However, according to the heat capacity of H2O, 3.7KJ will only...
14. ### Comparison of Change in Entropy

Upon seeing the question in my assignment I knew in a isobaric process, work done by the gas is ##W=P\Delta V## so if volume is increased ##4## times the original considering the original volume as ##V## we can say after expansion the volume is ##4V##. Then ##W=P(4V-V)=3PV## and the ##Q## would...
15. ### Instrument accuracy and comparison measurements

Hello, All measurement instruments have a finite accuracy. For example, a thermometer may provide a temperature measurement that is +-2F from the "actual" and true temp value. For example, if the reported measurement is 70F, the actual temperature may be between 72F and 68F. That said, let's...
16. ### I General relativistic comparison to Newtonian physics

Let's say a small object orbits around massive object at some distance in perfectly circular orbit. In Newtonian physics the force acted upon orbiting body is: Force = m1 * orbital_speed^2 / distance = G * (m1*m2) / r^2 for an object of 1kg orbiting a body of 2*30^kg at the distance of 1.521 *...
17. ### Potassium sodium tartrate preparation and comparison with recipes

Hi hi, here a question, how can we prepare Potassium sodium tartrate?, well, there is a lot of sites and videos, but in order to this right I'll write what have I done and checked, I'll try use the info I have, even if is not very dependable. First, we need sodium carbonate, to do this, we can...
18. ### Video: SF ships/structures size comparison

Here's a nice video which is a size comparion of a great number of fictional structures from science fiction novels, movies and games. The video is called "FICTIONAL STARSHIPS Size COMPARISON" but it includes some structures I personally wouldn't call starships, but anyway... Enjoy...
19. ### Tension forces of two wires in comparison to the gravitational force

The correct answer is the second one. I honestly have no idea why this is so. I understand that the right rope has less tension that the left one since it's at a shallower angle from real world experience, but I don't really know why this is so, let alone how the forces compare to gravitational...
20. ### Inducing electric current in a wire (a comparison)

Consider the following experiment: from a lacquered copper wire we cut off twenty to thirty pieces of about 10 cm. From them we form a bundle of parallel wires and connect the two ends with one more wire each. The other ends of these two wires are connected to a sensitive analog ammeter. We hold...
21. ### Comparison of Induction Heaters

As the summary says: I have 2 induction heaters which are exhibiting different results when heating the same product. The 2 are different, having different sized coils, and I would like to work out the strength of the induced field in each of them (with a common item being heated) to establish...
22. ### Hamilton's equation and Euler-Lagrange's equation comparison

We know that the momentum for such a lagrangian is: $$p_k = \frac{\partial L}{\partial \dot q^k} = 1/2 \Big( G_{ab} \delta_k^a \dot q^b + G_{ab} \delta_k^b \dot q^a\Big) = 1/2 \Big( G_{kb} \dot q^b + G_{ak} \dot q^a\Big) = G_{ak} \dot q^a$$ OK so using Hamilton's equation we get (and recalling...
23. ### Si IGBT and SiC MOSFET comparison

I am trying to understand the difference between an Si IGBT and SiC MOSFET. The device structure in question is the following: https://www.researchgate.net/figure/Comparison-between-Si-IGBT-and-SiC-MOSFET-modules-a-Cross-section-of-Trench-FS-Si-IGBT_fig6_318908365 It's hard to understand why...
24. ### Comparing a hydronium with a hydroxide in a weak acid solution (0.1M)

This question says: An HA weak acid solution with a molarity of 0.1M is dissolved in water. In the new solution, is the molarity of OH- greater than the H3O+ molarity, or the opposite? Or are they equal? I came up with two possible answers: 1. [H3O+]>[OH-] because there are no hydroxides...
25. ### I Comparing theoretical calculations with experimental data

Dear users, The situation I have encountered is a simple statistical comparison of the experimental data, which accepted as correct, with the results obtained via six theoretical models. In the experimental data, there exist y values corresponding to x values and also the measurement errors of...
26. ### MHB Comparison test on series

Use the comparison test to determine if the series series convergences or divergences $$S_{6}=\sum_{n=1}^{\infty} \dfrac{1}{n^2 \ln{n} -10}$$ ok if i follow the example given the next step alegedly would be... $$\dfrac{1}{n^2 \ln{n} -10}<\dfrac{1}{n^2 \ln{n}}$$ $\tiny{242 UHM}$
27. ### How to characterize mathematical models for comparison

I am reviewing and comparing a wide range of mathematical models that are being applied to a specific realm of wildlife biology. For the comparison of these models, and to weigh advantages/disadvantages of different aspects with regard to application, I need to characterize each model. As I do...
28. ### MHB First Comparison Test for Series .... Sohrab Theorem 2.3.9 ....

I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers ... ... I need help with the proof of Theorem 2.3.9 (a) ... Theorem 2.3.9 reads as follows: Now, we can prove Theorem 2.3.9 (a) using the Cauchy...
29. ### Comparison horizontal distance in presence of resistance

Homework Statement A particle of mass m kg is projected under gravity with horizontal and vertical components of velocity U and V. There is horizontal resistance of magnitude mku, where k is constant and u is horizontal component of the velocity at t seconds. No vertical resistance present. (i)...
30. M

### Mathematica 2D PDE Solution with Neumann BC: Plot Comparison

Hi PF! I'm solving a 2D PDE using NDSolveValueMesh. On one boundary I apply a Neumann BC. Attached are two plots: the top is the boundary condition and the functional value. Notice both are exactly the same. However, the lower plot shows a directional derivative evaluated on the same boundary...
31. ### Nuclear stability comparison

Homework Statement This is a conceptual question I have, the binding energy per nucleon is mass defect*c^2/mass number while the packing fraction is mass defect/mass number. A higher binding energy per nucleon indicates a more stable nucleus BUT a smaller packing fraction indicates a more...
32. ### Nuclear waste comparison between LWR and HWR

Hi, If we compare LWR and HWR (CANDU), which reactor type produces more waste per used Uranium? And also, between these reactors, is there a difference at the time required for the spent fuel to be completely safe? For LWR, It is around 100 000 years. But what about HWR? Thank you in advance.
33. ### Magnitudes and Comparison

Homework Statement You have decided to use a CCD camera to check if a 16th magnitude quasar is variable. With your telescope/camera combination, you know that a star with a magnitude of 0 would deliver 1 × 109 photons/second to one pixel, so this allows you to work out the photons/second from...
34. ### I Dimensions of the double slits in comparison to the electron?

what are the dimensions of the double slits in comparison to the electron? what keeps the electron from decaying outside the environment of an atom long enough to run the experiment? how are the electrons detected before and after the slits?
35. ### Atoms in Living vs. Dead Cells: A Comparison

I want to know what is the difference in atoms when a cell is alive and after it is dead
36. ### I Comparison of movement of Disc and Hoop

A disc and a hoop (ring) both of same mass and radius roll down an inclined plane of height "h". It is well known the disc has great velocity than that of the hoop at the bottom. I am fixed in the situation after they start rolling horizontally. Which will go farther? If the surface is...
37. ### Comparison of thermal shock profiles

Could someone help me in comparing 2 different thermal shock test profiles effect on a component. The 2 profiles are varied in deg C /min change and also the dwell time in low and high tempwratures. Any references are highly appreciated. Thank you
38. ### Comparison test of infinite series

Homework Statement Homework EquationsThe Attempt at a Solution So the book is saying that this series diverges, i have learned my lesson and have stopped doubting the authors of this book but i don't understand how this series diverges. ok i can use the comparison test using 1/3n and 1/3n...
39. ### MHB Carl Sontag's Interest & Discount Note Comparison

Carl Sontag wanted to compare what proceeds he would receive with a simple interest note versus a simple discount note. Both had the same terms: \$19,500 at 8 % for 2 years. Use ordinary interest as needed. A. Calculate the simple interest note proceeds. B. Calculate the simple discount note...
40. ### Does this series converge? Using the limit comparison test

The problem In this problem I am supposed to show that the following series converges by somehow comparing it to ## \frac{1}{k\sqrt{k}} ## : $$\sum^{\infty}_{k=1} \left( \frac{1}{\sqrt{k}} - \frac{1}{\sqrt{k+1}} \right)$$ The attempt ## \frac{1}{\sqrt{k}} - \frac{1}{\sqrt{k+1}} =...
41. ### Circuit comparison in everycircuit

Hi. Found a circuit pre made at everycircuit and tryed to reproduce it for scratch but the new circuit does not work. I am as new to electronics as one can be, so that is why i ask if i don't understand something with these circuits or is this probably a bug with everycircuit? In image left is...
42. ### Catalyst Comparison: B vs C

Hi, PF I have to comment this graphic about a reaction with and without catalysis. It's clear that the 'b' and 'c' line represent the catalysed processes, but I don't get one thing: my professor said that 'c' is a worse catalyst than 'b'. Why? Thank you
43. ### Insights The Schwarzschild Metric: Part 3, A Newtonian Comparison - Comments

Greg Bernhardt submitted a new PF Insights post The Schwarzschild Metric: Part 3, A Newtonian Comparison Continue reading the Original PF Insights Post.
44. ### Series Comparison Test for Divergence: sin(1/n) vs 1/(1+n)

Homework Statement ##\sum _{n=0}^{\infty }\:\sin \left(\frac{1}{n}\right)## Homework Equations The Attempt at a Solution Can I try comparison test by ##\left(\frac{1}{1+n}\right)<sin\left(\frac{1}{n}\right)## since ##\left(\frac{1}{1+n}\right)## diverges also...
45. ### I Comparison of tidal forces acting on the Moon vs Enceladus

I have heard about a moon Enceladus. Which is powered by tidal force. I suppose this force press back and forth on the moon and friction in the core causes heat. I hope I'm right :-) Now tidal force ##F_t=\frac{2GMmr}{R^3}##, where ##G## is Gravitation constant, ##M## is mass of planet causes...
46. ### I Comparison of Moving Masses

Here there are two scenarios for comparison. Scenario 1: We move two connected masses which are Constantly 3 metres apart on a friction free surface using the same force and acceleration in a straight line. Scenario 2: We move two connected masses which are Constantly 3 metres apart over an...
47. ### Comparison of Cs, Sr and Pu fallout from meltdown

I combined three maps of Chernobyl fallout: Cs-137 map, Sr-90 map and Pu-239 map. Map scales are the same. Lowest contour levels for Cs and Sr are the same (1 Ci/km^2), Pu contour is ten times lower (0.1 Ci/km^2). This visually demonstrates that Cs is about ten times more widespread fallout...
48. ### Compare LHS and RHS: Solve Problem Equation

Homework Statement LHS (3y+2)/5 RHS y Which is greater? Homework Equations Equation is provided in the question The Attempt at a Solution let y=1: LHS= 1 RHS=1 So LHS & RHS are equal. 2ND try; LET Y=0 LHS= 0.4 RHS= 0 So LHS is greater. So Answer can't be determined using the information...
49. ### Comparison of high-level computer programming languages

A little question about the appropriateness of a certain research subject... Would it be useful to make a study of the computational effectiveness of equivalent codes written with Matlab, Mathematica, R Code, Julia, Python, etc. in a set of typical computational engineering problems like...
50. ### Comparison of Different Mammalian Brains

This shows brains from several different (mostly primates and rodents) at the same scale. Obtained from here. The weight is listed in grams, the (purported) number of neurons is in millions(M). Estimates of neuronal numbers are difficult. Sadly they are not all pointing the same direction.