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. fluidistic

    Probability, QM, harmonic oscillator, comparison with classical

    Homework Statement I must calculate the probability that the position of a harmonic oscillator in the fundamental state has a greater value that the amplitude of a classical harmonic oscillator of the same energy.Homework Equations ##\psi _0 (x)=\left ( \frac{m \omega}{\pi h } \right ) ^{1/4}...
  2. alyafey22

    MHB Can improper integrals converge without absolute convergence?

    I know we have the following \big | \int^{b}_{a} f(t) \, dt \big | \leq \int^{b}_{a} |f(t)|\, dt 1- How to prove the inequality ,what are the conditions ? 2- Does it work for improper integrals ?
  3. P

    Proving Convergence of Direct Comparison Test for \sum \frac{3}{n^{2} + 1}

    Homework Statement Show that: \sum \frac{3}{n^{2} + 1} converges from n = 1 to ∞ Homework Equations If Ʃbn converges, and Ʃan < Ʃbn. Ʃan also converges. The Attempt at a Solution \sum \frac{1}{n^{2}} converges \sum \frac{3}{n^{2} + 1} = 3 * \sum \frac{1}{n^{2} + 1}...
  4. T

    Comparison Test problem with infinite series

    Homework Statement I need to use the Comparison Test or the Limit Comparison Test to determine whether or not this series converges: ∑ sin(1/n^2) from 1 to ∞ Homework Equations Limit Comparison Test: Let {An} and {Bn} be positive sequences. Assume the following limit exists: L =...
  5. I

    Does Gravity Affect the Passage of Time on Different Planets?

    If one planet has a higher gravity than another, would that mean that it would progress through time at a slower rate than the other, being 'deeper' in a gravity well? That it would 'age' slower, relatively?
  6. T

    How to Use Comparison Test for Convergence?

    Homework Statement Is the series convergent or divergent? \sum_{n=0}^{\infty}{\frac{1}{\sqrt{n+1}}} Homework Equations I can use any test but wolfram alpha says that it is divergent by comparison test. The Attempt at a Solution How do I apply comparison test? I can compare it to: \sum _{...
  7. P

    Comparison Theorem and Limits of integration

    Homework Statement Why is it that when using the comparison theorem my limits of integration must be from a constant value to infinity and not from negative infinity to infinity? For example ∫ x/(1+x^2) dx from -∞ to ∞
  8. K

    Comparison vs. limit comparison vs. sum splitting

    I'm not really sure when each of these should be done. In fact, I don't really understand the reason that we use the limit comparison test. Σ1/(n^2+1) So here I can simply say that P=2>1, so the original converges. Σ1/N^3+N^2 Here, I would say that P=3>1, implying the original...
  9. W

    Convergence of tan(1/n) using Direct Comparison Test

    Homework Statement Use any test to determine whether the series converges.Homework Equations \displaystyle \sum^{∞}_{n=1} tan(1/n) The Attempt at a Solution Direct Comparison Test tan(1/n) > 1/n By integral test: 1/n diverges thus, by dct, tan(1/n) diverges.
  10. E

    What is the comparison rate for this homeloan?

    Hi guys, Just doing a few calculations on a homeloan and comparison rate calculation has got me stumped. Loan Amount: $320,000 Loan Time: 30 years Interest Rate:5.55% Initial Costs:$4463 Monthly Fee: $15 So from this, with a fortnightly compounding frequency, I calculate the total...
  11. P

    Evaluating Improper Integral with limits and comparison theorem

    Homework Statement evaluate the integral 1/(u^2 -36) from 0 to 6 does the integral converge? Homework Equations The Attempt at a Solution integral 1/(u^2 -36) integral 1/((u-6)(u+6)) Partial fraction decomposition 1/((u-6)(u+6)) = A/(u-6) + B/(u+6) 1=A(u+6) + B(u-6) 1=(A+B)u +(6A-6B) A+B=0...
  12. W

    Does the Limit Comparison Test Work for Divergent Integrals?

    Homework Statement use limit comparison test. Homework Equations \displaystyle\int_2^∞ {\frac{1}{\sqrt{x^2 - 1}} dx} The Attempt at a Solution I have tried usin 1/x as the comparison function, but when applying the test it comes out to 0, not an L -> 0 < L < ∞
  13. M

    Conservation of Energy: Comparison between momentum & magnetic fields

    Momentum and magnetic fields are both vector quantities. If two bodies with the precise mass and speed collide head on (θ = 0), then momentum is conserved (they come to a complete stop) and energy is conserved (the kinetic energy is changed to other forms). What then happens in the case of...
  14. W

    Convergence of Integral Using Limit and Direct Comparison Tests | Homework Help

    Homework Statement Use direct comparison test or limit comparison test to determine if the integral converges.Homework Equations \displaystyle\int_0^6 {\frac{dx}{9-x^2}} The Attempt at a Solution If i were to use the limit comparison test, would these integrals fit the criteria. ** if the...
  15. G

    Converging Series for ln(n) with Comparison Tests

    Homework Statement Find all positive values of b for which the series Ʃ bln(n) converges. Bounds are from n=1 to infinity. Homework Equations The assignment is for Direct Comparison Test and Limit Comparison Test. The Attempt at a Solution I don't know where to begin. Using a comparison...
  16. Y

    RE: vehicle weight, HP, and gearing comparison between vehicles

    Hello all. I am now enrolled at VRI at WWU! I am working on a sort of independent study project. I am making a V12 out of a pair of motorcycle engines to go into a VW based kit car. I have run the IHP formula and come out with 250hp, and 220 lb/ft of torque. The car weighs 1800 pounds...
  17. G

    Comparison of direction of forces

    Homework Statement if we apply a force of 56 n on 40 degree angle above the horizontal than how would the results compare if it was applied 40 degree below the horizontal?Homework Equations none The Attempt at a Solution i said that it would be the same and different depending on how we look...
  18. T

    Comparison between ideal, linear and lowpass filter interpolators

    Homework Statement Q3. Sampling and reconstruction A) It is common practice to use low order low pass filters instead of a Sinc filter, at the expense of a higher sampling rate. Here we investigate how to do this. Compare: a) the ideal reconstruction of a low pass sampled signal, which can be...
  19. L

    Comparison between aluminium and stainless steel

    I am looking for a paragraph on each metal on the comparison of aluminium and stainless steel under the heading: Manufacturing Methods: What processes are available to turn the raw material into products and how do the processing methods differ? Regards, Lockyphysics
  20. T

    Can someone explain the direct comparison test to me in detail?

    Homework Statement A few examples done in class that I didn't understand are as follows: (Find out if convergent or divergent) integral 0-->infinity ( x / (x^3 + 1) ) integral 1-->infinity ( (2+e^(-x) ) / x ) Homework Equations None The Attempt at a Solution Basically, I have NO idea...
  21. I

    Using Limit Comparison Test to Determine Convergence/Divergence

    Homework Statement Using the limit comparison test to determine convergence or divergence (1) \sum^{\infty}_{n=1} \frac{(ln(n))^{3}}{n^{3}} (2) \sum^{\infty}_{n=1} \frac{1}{\sqrt{n} ln(x)} (3)\sum^{\infty}_{n=1} \frac{(ln(n))^{2}}{n^{\frac{3}{2}}} Homework Equations...
  22. T

    Comparison of T, E and V in different states?

    Homework Statement The Attempt at a Solution I currently think that a and e are correct. But I am not sure what happens to the energy IN THE BOX. When the box explodes, the energy of the contents changes from potential to thermal, sound and kinetic energy. Thus by conservation of...
  23. N

    Magnifying Glass and Eye Glasses Comparison

    Do glasses work in the same way that a magnifying glass does. They take light and focus it onto a point? If a magnifying glass can burn an ant, do eye glasses burn our eyes to a certain degree? Could it just be that eye glass wearers don't stare at the sun? I hope you guys understand what I...
  24. A

    Multiple Languages - Comparison Thread

    Are you familiar with multiple languages? This is the thread to discuss what languages you like the best, what advantages/disadvantages they have over others, etc. I am familiar with C, Python, Ruby, Scratch, and JavaScript. That's all I can think of. IMHO: Python and Scratch definitely...
  25. S

    Does QM itself prevent removal of noise without comparison

    Is there some fundamental fact of the universe (Quantum Mechanics) that prevents us from removing noise (without having to compare the entangled particles)? In the quantum eraser experiments: To get ("un-embed") the interference pattern i.e. to separate the entangled particles from the...
  26. R

    Comparison test on second species integrals

    Homework Statement Determine if the following integrals are convergent or divergent. Explain why. \int^{1}_{0} \frac{1}{1-x^{4}} dx The Attempt at a Solution I've tried using Comparison Test, using f(x) = \frac{1}{1-x^{4}} and\; g(x) = \frac{1}{1-x}, 0 \leq f(x)\leq g(x) in ] 0,1 [ and I...
  27. A

    Comparison of two engines of the same displacement

    Hi all, I have this question, and hope you could help me to solve. There are two engines with the same displacement (say 250cc). One with smaller piston and the other bigger. Of course the first one will move longer. If everything else is the same or similar, generally, which engine is...
  28. AGNuke

    Strength comparison of Para/Dia-magnetism

    Which one of the following weighs less when weighted in magnetic field? A>SnCl3 B>FeCl3 C>TiCl3 D>VCl3 This is the question I encountered in my Chemistry Olympiad. While I went with B, my institute published answer as A. What I deduced is that A is diamagnetic while the rest are...
  29. L

    Comparison Test and Geometric Series

    The Problem: Let a(n) = (n^2)/(2^n) Prove that if n>=3, then: (a(n+1))/(a(n)) <= 8/9 By using this inequality for n = 3,4,5,..., prove that: a(n+3) <= ((8/9)^n)(a(3)) Using the comparison test and results concerning the convergence of the geometric series, show that: The...
  30. A

    Essentially comparison of isothermal and adiabatic transformations

    Homework Statement Two identical samples of ideal gas are initially at P1 and V1. The first sample undergoes an isothermal transformation to P2, V2 and second sample undergoes an adiabatic transformation to P3, V2. If P3<P2, is V2 higher or lower than V1? Explain Homework Equations...
  31. G

    Comparison between bulk and ac resistances of a diode.

    Hellow guys! I find this concept really confusing, if the bulk resistance of a diode is an approximation of the I-V characteristic curve for a diode, Why then is that bulk resistance compared to ac resistances of the same diode at a particular operating in calculated values, seem not to...
  32. M

    Improper integral using comparison theorem

    State if the following integral converges or diverges, and justify your claim. \int_{-1}^{1} \frac{e^x}{x+1}\,dx I tried using the comparison theorem by comparing it to \frac{1}{x+1} . But for the interval (-1,0) the function is smaller for all x. So I could not conclude whether it...
  33. E

    Limit Comparison Test: Does Order Matter?

    I was just wondering for the limit comparison test does it matter which function is on the top and bottom?
  34. N

    Hp vs weight; acceleration comparison

    I am working on an engineering project for college and have run into an unexpected wall. I thought that my approach would work, but I'm not sure if I am getting reliable results and wanted to check on the proper method. I am trying to calculate how long it would take a mass to accelerate...
  35. T

    Why is Density Necessary in the Viscosity Comparison Method?

    Hi,I don know if my question will be clear,but I will try it.So,I m wondering how was derive this equation: viscosity=viscosity(known liquid)*density(known from table)*time(liquid will get over one point of Ubelohde viscometer to second point of viscometer(unknown liquid)/density(known...
  36. M

    Limit/Direct Comparison for Series Question

    Homework Statement \sum_{n=1}^{\infty} \frac{7n}{6n^2 ln(n)+2} Determine whether the series converges or diverges.Homework Equations Denominator is growing faster, so the limit as n --> to infinity should equal zerioThe Attempt at a Solution I tried isolating the highest power of the both the...
  37. 9

    Exploring the Mysteries of Black Holes: Comparing the Phenomenon to a Lit Fire

    This may sound very silly and a tad bit hard for me to explain, but here goes! I have experienced and seen how when a lit fire was covered with a container, the oxygen begins to dissipate and it begins to suck things into the space. (I did not light myself on fire!) So I was wondering if...
  38. E

    Structure of Dolphin Brain and Comparison to Primates?

    Dolphins have larger brains than humans. So, why aren't they smarter than humans... or, are they? Are those sneaky Dolphins playing dumb? j/k It's my (very limited) understanding that the cortex is responsible for the higher levels of what we think of as intelligence. So, what's different...
  39. T

    Which Is Faster: A 2000 HP Car or a 500 HP Enclosed Motorcycle?

    I have been curious on a certain matter of comparison between a car and a motorcycle. if your took a car and a enclosed motorcycle ( for aero and top speed )lets say for hypothetical purposes the car weighed 2000 lbs and had 2000 horsepower, while the bike weighed 500 lbs and had 500...
  40. E

    Real vs. Virtual Photons: A Comparison

    What is the difference between real photons and virtual photons?
  41. Redbelly98

    Temperature scale comparison

    Pretty funny stuff! https://sphotos-b.xx.fbcdn.net/hphotos-ash4/309379_450399368314413_942684559_n.jpg
  42. A

    Exploring the Milne Universe in 2D: Rindler Spacetime Comparison

    I'm studying the Milne Universe in two dimensions. The metric is similar to that of Rindler spacetime, but with time and space inverted. ds^{2}=-dt^{2}+t^{2}dx^{2} The Carter Penrose diagram of this spacetime would be the same of Rindler spacetime?
  43. S

    Payload dimension comparison between launch vehicles?

    Hey guys, Does anyone have a list of the maximum dimensions of objects that can be carried in various launch vehicles, eg Falcon 9/Falcon Heavy, space shuttle etc? It would be much appreciated!
  44. N

    MATLAB MATLAB Image Comparison Methods

    I'd like to know how to compare two greyscale images with each other using MATLAB. These two images for simplicity sake will both be circles and of different intensities. I need to be able to figure out by what proportion one image's intensity is of the other. For instance with 8-bit...
  45. M

    Proof of Convergence by Integral Test and/or Comparison Test

    Note: This is not strictly a homework problem. I'm just doing these problems for review (college is out for the semester) - but I wasn't sure if putting them on the main part of the forum would be appropriate since they are clearly lower-level problems.(Newbie) Homework Statement The...
  46. F

    AM and DSBSC waveform comparison ?

    Hello, I am wondering what sort of visual differences you would see between an AM modulated waveform with carrier and a DSBSC waveform (suppressed carrier) in the time domain on an oscilloscope. Any help would be appreciated.
  47. M

    Comparison vibration level of nylon and pvc pipe

    Homework Statement comparison nylon and pvc pipe which one vibration level is higher ? depend on which material properties ? Homework Equations The Attempt at a Solution
  48. A

    Taylor and Euler Matlab Comparison for Numerical Analysis.

    1. Solve y'=3t^2y^2 on [0, 3] , y0 = −1, using Euler method and Taylor method of order 3. Compare your solutions to the exact solution. y(t)=(-1/((t^3)+1)) I DONT KNOW WHAT IS WRONG WITH MY PROGRAM! PLEASE HELP =D Homework Equations http://en.wikipedia.org/wiki/Euler_method...
  49. I

    Exploring Net Annual Cost of Investments: A Comparison

    I've been searching everywhere for an answer to this question but haven't been able to get one. Let's say we're coming two things at 12% compounded annually. A's investment, salvage, life, and expense/year are given as: $50,000 ; $10,000 ; 11 ; $5000 While B's are: $40,000 ; $0 ...
  50. B

    Comparison b/w work done in adiabatic & isothermal processes

    Homework Statement In the graph attached, why is isothermal graph line higher than adiabatic one?? Homework Equations The Attempt at a Solution At first, i had thought that work done in an isothermal process is greater than in an adiabatic process...but for comparison we would...
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