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. C

    Using Comparison Theorem to solve a problem

    Homework Statement Use the Comparison Theorem to evaluate whether Integral(dx/(x*sinx)) on 0->pi/2 converges or diverges. The Attempt at a Solution I don't understand what to do about 0. Am I allowed to compare it to 1/x even though 1/x is undefined at 0? Like-wise am I allowed to...
  2. V

    Question about the comparison test

    Homework Statement determine whether the series diverges or converges (∞,n=1) ∑ (n2 - 1)/(3n4 +1) Homework Equations The Attempt at a Solution (∞,n=1) ∑ (n2 - 1)/(3n4 +1) an = (n2 - 1)/(3n4 +1) i thought bn should be n2/3n4 = 1/3n2 lim n-->∞ an/bn = (n2 - 1)/(3n4 +1) * 3n2 lim n-->∞...
  3. F

    Size comparison, from the moon to the largest known star

  4. T

    Data comparison and noise measurement

    Hi, I would like to measure the signal noise in a tv cable after introducing a splitter and compare it with the original signal. Keeping in mind the bandwidth frequency of the tv cable signal transmission, what kind of instrument do I need? Oscilloscope perhaps? At what speed? I don't know...
  5. A

    Comparison between PIC16 and Atmel ATmega

    Hi This a question from one of my exam papers.I searched all over internet but couldn't find any article or information source comparing atmel vs PIC in following manner. all i could find was threads talking about which is better.none of them discussed the matter with respective to following...
  6. J

    Comparison of asymptotic behavior of two Lebesgue integrals.

    Homework Statement The problem is to show that \int_1^x \frac{| \sin(t) |}{t} dt \underset{x \rightarrow \infty}{\sim} \frac{2}{\pi} \log(x). The integral is (in case it is important) a Lebesgue integral. Homework Equations A theorem is stated which says (I do not currently have the...
  7. FtlIsAwesome

    Comparison of thermonuclear and antimatter explosions of equal yield

    Hi This is my first post, and I have a lot of ideas to talk about I'll start with this one: What would the difference be between a thermonuclear explosion and an antimatter explosion, of equal yield (say 2 megatons each), and similar location and weather? I think that the each would have a...
  8. T

    Comparison Test on Interval 0 to 1

    Homework Statement Determine whether or not the integral from 0 to 1 of (5ln(x)) / ( x^(3/2) ) converges or not. Homework Equations The Attempt at a Solution I just need to know which end of the integral they are talking about. As x=>0, y=>-infinity. As x=>1, y=>1. I'm assuming...
  9. T

    Comparison Test: converges or diverges?

    Homework Statement Determine whether or not the improper integral from 0 to infinite of (e^x)/[(e^2x)+4] converges and if it does, find it's definite value. Homework Equations The Attempt at a Solution I missed the lecture on the Comparison Test, so I'm essentially useless. I...
  10. G

    Comparison of Electric and Magnetic Forces

    Homework Statement Suppose that the instantaneous velocities of two positive point charges are parallel. Compare the electric and magnetic forces. Show that the ratio of the magnetic force (Fmag) to the electric force (Felec) is: Fmag/Felec = v1*v2/c^2 Where v1 and v2 are the velocities of...
  11. A

    Negative One vs Seven: A 2's Complement Comparison

    in 2's complement the negative of 1 is "111". but it also signifies 7 in decimal. how does this -ve 1 is differ from 7? thanks
  12. R

    What did i do wrong? Ratio and comparison test question?

    Homework Statement The summation of n/lnn from n=1 to infinity Homework Equations Ratio and Comparison test The Attempt at a Solution http://i55.tinypic.com/2jxuue.jpg Alright so the way labeled "right way" on the picture is the right way according to the book but isn't the...
  13. L

    Comparing Wheel Speeds for Traction Control

    Hi, I am experimenting with traction controlling of wheels. I have to calculate the speed difference in two wheels (driven and non-driven). I am thinking of these options: 1. Generate pulse train using optical encoder -> binary counter -> D/A converter -> Take voltage difference using OP...
  14. M

    Limit Comparison Test for Series

    Just a general question, but I find it hard to come up with a b[n] to compare to a[n]. When the book does it, they come up with stuff to compare to a[n] that I would have never thought of. Is there any criteria, things to look for, etc., for coming up with a b[n] to compare to a[n]?
  15. M

    Limit Comparison Test for Divergence: Solving Problems with a_n/b_n

    Homework Statement \sum_{n=1}^\infty \frac{1+4^n}{1+3^n} where a_n= \frac{1+4^n}{1+3^n} and b_n= \frac{4^n}{3^n} Homework Equations I know how to do this problem, you take the limit as "n" goes to infinity of a_n/b_n ... which after a good amount of algebra ends up being 1...
  16. M

    Finding a and b in an infinite series limit comparison test

    Finding "a" and "b" in an infinite series limit comparison test Homework Statement \sum_{n=1}^\infty \frac{\sqrt{n+2}}{2n^2+n+1} How do I identify my a_n and my b_n? In this particular problem you need to use the Limit comparison test which is your "a_n" divided by your "b_n". I...
  17. P

    Limit Comparison Test for Convergence or Divergence: (n+5)/(n^3-2n+3) and n/n^3

    Homework Statement show whether \sum (n+5)/(n3-2n+3) is convergant of divergant Homework Equations limit comparison test, lim an/bn = c where c > 0 The Attempt at a Solution an is given let bn = n/n3 so then: lim (n+5)/(n3-2n+3) n/n3 = lim (n+5)n3 /...
  18. I

    Age comparison to observer on Earth (time dilation)

    Homework Statement Alpha Centauri is about 4 light years from the Earth. If you were to travel to Alpha Centauri and back at the speed of the electron that you calculated in question A (0.780c), how much would you age compared to an observer on Earth? Homework Equations There equations...
  19. silvermane

    Comparison Proof via axioms, almost done need hints for finish and proof read

    1. The problem statement: Prove that 0\leq2x^2 - 3xy + 2y^2 2. These are the axioms we are permitted to use: 01) Exactly one of these hold: a<b, a=b, or b<a 02) If a<b, and b<c, then a<c 03) If a<b, then a+c < b+c for every c 04) If a<b and 0<c, then ac<bc. The Attempt at...
  20. A

    Need statistical data for comparison with my simulation

    Hello, I'm new to this forum so I don't really know if this is the correct section for this question, but I couldn't find anything that fits better. I'm in my last year in school and writing a program for an extended essay (at least that is what google tells me is the translation for the...
  21. P

    Comparison Tests of Convergence 1 + 1/1 + 1/2 + 1/3 + · · ·?

    Homework Statement question given is 1 + 1/1! + 1/2! + 1/3! + · · · the question need to be compared with another equation so how to get the second equation? Homework Equations n/a The Attempt at a Solution i duno homework to startT.T
  22. D

    RGB Color Comparison: Find Closest Matching Color

    Say you had a color picked out and a list of different colors that you wanted to find the closest matching color from. Is anyone aware of some formula to do this for computer RGB colors?
  23. O

    Compatibility comparison: ethyl alcohol vs. denatured alcohol

    I have plastic, metal and rubber parts that are compatible with ethyl alcohol (they are regularly washed in a bath of ethyl alcohol). I’m looking for a substitute solution to wash these parts and I am considering denatured alcohol, however, I’m concerned that the denaturing ingredients will...
  24. D

    Direct Comparison Test inequality help

    Homework Statement Explain why the Direct Comparison Test allows us to use the inequality Ln n < n^(1/10) even though it is not true for a great many n values. Homework Equations The Attempt at a Solution I looked at the graphs of Ln (n) vs. n^(k)
  25. F

    Heat over time comparison question

    I have a fairly basic (I hope) question - please note that the values given are just to make the problem easier to comprehend: Given: I'm heating, via convection, a constant sized spherical mass (Let's say m=1g) with a consistent surface area (Let's say SA = 1cm^2) at a constant...
  26. C

    Convergence comparison test (sequence, calc II)

    Homework Statement Finally done with stupid improper integrals (calc 2 over summer is hard work, moving super fast) and now I'm sequences and series and what have you. I have another comparison test problem Instructions are to find out if sequence converges or diverges, and find limit if it...
  27. S

    Comparison Test Question: How to Determine Convergence of a Complex Integral?

    Homework Statement I'm just curious as to how to think about the following form of equation. Homework Equations \int_{3}^{\infty } \frac{1}{x + e^x} \,dx The Attempt at a Solution What you're trying to do is to test it; \frac{1}{x \ + \ e^x} \ < \ \frac{1}{x} \frac{1}{x}...
  28. R

    Calculating the Shortest Distance to the BZ Boundary for Electron Energy Comparison

    Hi, I just can't understand the basics with BZ. How do I find the shortest distance to the BZ boundary, how do I compare the electron energy between the last electron in the 1st BZ with the first electron in the 2nd BZ? I think I need a visual how to calculate these things, does anyone...
  29. Orion1

    Size comparison of WASP-12b (gray) with Jupiter.

    Size comparison of WASP-12b (gray) with Jupiter. http://d.yimg.com/a/p/afp/20100524/capt.photo_1274732261799-1-0.jpg Reference: http://en.wikipedia.org/wiki/WASP-12b" http://en.wikipedia.org/wiki/WASP-12" [PLAIN]http://news.yahoo.com/s/afp/20100524/ts_alt_afp/usscienceastronomy"
  30. X

    Comparison of Modulation Techniques

    Hi guys, I'm new to the forums and hope someone can help with this. Homework Statement Compare the modulation techniques used by 2 different applications, giving reasons for their use. Use data tables, diagrams and any other sources to help Homework Equations None The Attempt...
  31. G

    Comparison of 4 sets of data: a measure of similarity

    hi, i measured the emission spectrum of an LED with a monochromator connected to a PMT tube. the spectrum was measured at four different gain levels on the PMT. i want to check the PMT's linearity at the different gain level, so i want to compare the four data sets and check their...
  32. Z

    Use comparison theorem to show if integral is convergent or divergent

    Homework Statement int (e^-x)/(x)dx from 0 to infinity Determine if integral is convergent or divergent2. The attempt at a solution I assume because the bottom limit is 0 and there is an x in the bottom of the integral that this is going to be divergent but I still have to use the...
  33. C

    Comparison of Physics Departments

    Hi, so I have a question that has been plaguing me for the longest.. I am a high school senior and I hope to Major in Physic when I enter college, yet I am torn between two schools. Georgia Institute of Technology vs. Jackson State University Now, I can be pretty sure of the obvious...
  34. A

    Quick Question on Limit Comparison Test

    Can the limit comparison test work on alternating series? I looked at the conditions online and it said that the series a_n and b_n must be > 0 in order to use it. To be specific it said, "Suppose that a_n > 0 and b_n>0 for all n> or = to N (N a positive integer)." I asked my teacher about this...
  35. L

    Convergent or Divergent Integral: Comparison Theorem

    Homework Statement Determine if the following is improper and convergent, improper and divergent, or proper \int \frac{dx}{\sqrt[3]{x^2 - 7}} from 8 to infinityThe Attempt at a Solution Since I don't know how to integrate...
  36. M

    Comparison between mobile systems?

    what are the main differences between the 2nd generation (GSM) system and the 4th generation, in terms of: -the type of modulation used. -multiplexing with the base station. -bit rate and bandwidth given for each supscriber. - the complexity of the system. if you could provide links for...
  37. R

    Help with problem, comparison of energy released

    Using the equation Force = Pressure x Area. How much energy would be released from an iron tube 48” long with an inside diameter of 2.1” and outside diameter of 3”. Wall thickness would be .9”. With 8500psi inside. Maybe I calculated it wrong but I got 1.1 million pounds of force released. Once...
  38. S

    Motion of Train vs Platform: A Radiation Comparison

    the frequency of radiation emitted when electron and positron are annihilated in the moving carriage is more than the the frequency of radiation emitted when the same experiment is done on railway platform .Is it not enough to decide that the motion of the train is real while platform motion is...
  39. P

    Electric field strength of a wire comparison

    1. Homework Statement The electric field strength 7.79 cm from a very long charged wire is 2660 N/C. What is the electric field strength (in N/C) 12.7 cm from the wire? 2. Homework Equations E= (9*10^9) Q/ r^2 3. The Attempt at a Solution i have energy. so is tried to solve...
  40. M

    Improper Integral using Comparison to determine Convergence/Divergence

    Homework Statement Use a comparison to determine if the improper integral converges or diverges. If the integral converges, give an upper bound for the value. Integral of d(theta) / (theta^3 + theta)^1/2 from 1 to infinity Homework Equations N/A The Attempt at a Solution I'm...
  41. I

    Help understanding Direct/Limit comparison tests

    I'm having an extremely hard time understanding direct/limit comparison tests, and i will post some questions so you guys can attempt to help me. integral from 0 to pi of: dt/[sqrt(t) + sin(t)] and integral from -infinity to infinity of: dx/[ex + e-x] I cannot show my work because i...
  42. F

    A comparison on binomial expansion

    Could anyone help me on this question? Is it true that \sum_{k=n+1}^{2n}\left(\begin{array}{c} 2n\\k\end{array}\right)x^{k}\left(1-x\right)^{2n-k}\leq2x for any x\in(0,1) and any positive integer n? Any help on that will be greatly appreciated!
  43. K

    Minkowski diagram frame scale comparison

    Homework Statement Draw a clearly labelled “Minkowski spacetime” diagram illustrating two events ((1) a farmer firing his laser gun at his cow, which is sitting along his positive x-direction, and (2) the cow dying) as observed by two observers (S at rest in the farmer’s and cow’s frame, and...
  44. M

    Does Object Configuration Remain Consistent After Relativistic Transport?

    When we are taught relativity we never seem to be asked to consider how the configuration of objects in frames moving relative to ours actually got there. It just seems that we imply that is the way they always were and so an actual congruence measurement of direct comparison in the same frame...
  45. C

    Which software is best for PIMD simulations: PINY or CPMD?

    I am planning to do some simulations using path integral molecular dynamics approach. I have never used it before, so I would like to have some information concerning packages that are used for that kind of simulations. I am aware of PINY and CPMD packages for PIMD. Which one is better? Are...
  46. P

    Series Comparison Test for (n^n)/n! and Convergence Analysis

    Homework Statement Find if the sum from n = 1 to infinity of (n^n)/n! diverges or not. Homework Equations p = an+1/an The Attempt at a Solution Using the comparison test I get to the point where p_n = (n+1)^(n+1) / [(n+1) n^n] Shouldnt p just be 0, don't (n+1)^(n+1) and n^n...
  47. I

    Finding the Upper Bound for a Convergent Series: A Comparison Method

    Homework Statement I need to show that: \sum_{n=1}^\infty \frac{n^{2}}{2^n} converges. I know I can compare it with the larger convergent geometric series: \sum_{n=1}^\infty \frac{1.5^{n}}{2^n} Which is larger for all terms for n> 13. My question is, I found this "13" through trial and...
  48. G

    Comparison and Limit Comparison Tests for Convergence of Series

    Homework Statement \sum^{\infty}_{n=1} \frac{e^{n}+n}{e^{2n}-n^{2}} Homework Equations I have to use either the Comparison Test or the Limit Comparison Test to show whether the series converges or diverges. The Attempt at a Solution a_{n} = \frac{e^{n}+n}{e^{2n}-n^{2}} b_{n} =...
  49. P

    Comparison Test for Infinite Series Example

    Homework Statement Using the comparison test determine if the infinite series for sin(3/n^2) converges or diverges. The Attempt at a Solution Well... these are pretty straight forward, and it's pretty obvious that this is convergent, but I'm having trouble applying the...
  50. G

    Infinite Series Comparison Test

    I read a proof for showing that the harmonic series is a diverging one. This particular one used a comparison test: 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + ... + 1/16 + ... 1/2 + 1/2 + 1/4 + 1/4 + 1/8 + 1/8 + 1/8 + 1/8 + 1/16 +... + 1/16 + ... Each term in the second series is <...
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