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. K

    Comparison test for series convergence (trig function)

    Homework Statement Use a comparison test to determine whether this series converges: \sum_{x=1}^{\infty }\sin ^2(\frac{1}{x}) Homework EquationsThe Attempt at a Solution At small values of x: \sin x\approx x a_{x}=\sin \frac{1}{x} b_{x}=\frac{1}{x} \lim...
  2. K

    Use comparison test to see if series converges

    Homework Statement \sum_{x=2}^{\infty } \frac{1}{(lnx)^9} Homework EquationsThe Attempt at a Solution x \geqslant 2 0 \leqslant lnx < x 0 < \frac{1}{x} < \frac{1}{lnx} From this we know that 1 / lnx diverges and I wanted to use this fact to show that 1 / [(lnx) ^ 9] diverges but at k...
  3. F

    Yielding vs buckling comparison

    Homework Statement http://www.continuummechanics.org/eccentriccolumnbuckling.ht In here , i was told that for the eccentrically loaded column , the column will fail due to before it buckles . How is that possible ? Homework EquationsThe Attempt at a Solution The column will start to buckle...
  4. B

    Compare & Determine: The 1/n! Series Convergence/Divergence

    Homework Statement Determine whether the series converges or diverges. ∞ ∑ 1/n! n=1 Homework Equations If ∑bn is convergent and an≤bn for all n, then ∑an is also convergent. Suppose that ∑an and ∑bn are series with positive terms. If lim an = C n→∞ bn where c is finite number and c>o...
  5. R

    B De Broglie Wavelength & Classical EM Wavelength Comparison

    Under what condition would particle de Broglie wavelength be equal to the classical EM wavelength?
  6. chastiell

    I About comparison to experimental reference values

    Hi again, probably this seems to be a simply question, but in last days i becomes a really strange one. We all know that there are many kinds of constants in physics, some of them, are found experimentally with great accuracy in too expensive projects, but no matter how accurate can be measured...
  7. M

    Comparison of internal energies: hot nail versus beaker of water

    Homework Statement [/B] A nail is heated in a bunsen burner flame and is about to be dropped into a beaker of water at room temperature. a) Which of the two substances (nail or water) would you expect to initially have: i) the highest internal energy ii) the highest average kinetic...
  8. P

    Abaqus - Boundary Conditions Comparison of two models

    Hi everyone, This is my first time posting here I am looking to get some help with Abaqus, I wish to compare two models and find the residual stress which causes a original model to deform to the other. The deflection between the two models can be calculated by other software. I plan to do...
  9. VNN

    Programs Physics or Engineering comparison?

    I love physics/maths/ETC.. I'M considering physics and doing relevant preparation(Only in y11(15 years old))... Just wondering if there are any benefits to engineering in comparison? This include all aspects like satisfaction/pay/Amount of science involved/ETC...? Thanks
  10. karush

    MHB Is the Integral of ${x}^{2}/({x}^{5}+2)$ Convergent or Divergent?

    71. Use the Comparison Theorem to determine weather the integral $$\displaystyle I=\int\frac{{x}^{2}}{{x}^{5}+2} \, dx$$ is convergent or divergent. Comparison Theorem Suppose that $f$ and $g$ are continuous with $f(x) \ge \, g(x) \ge 0 $ for $x\ge a$ (a) if $\displaystyle \int_{a}^{\infty}...
  11. physea

    I Comparison of solid and hollow cylinder

    Hello! We have a solid cylinder and then we take that and drill its core so that it becomes hollow. In which case the cylinder will be stronger? Thanks!
  12. A

    Programs Which European Master's Programs Are Best for Theoretical Particle Physics?

    hello everyone, i am currently a physics undergraduate in europe and i am thinking about possible graduate studies either in usa or europe.i want to study theoretical particle physics(string theory,quantum fileds,cosmpology etc.). my first choice is a phd in usa. but as an alternative i am...
  13. S

    Load Bearing Capacities of Steel Rods & Ropes: A Comparison

    Consider a steel rod of diameter 'd'. If the same rod is broken up into strands and arranged parallel to one another so as to form a new rod of the same diameter 'd' ,Which will have a higher load bearing capacity?. Instead of being arranged parallel , If they are made into a rope of similar...
  14. T

    MHB Limit Comparison Test: Does L Approaching Infinity Matter?

    The limit comparison test states that if $a_n$ and $b_n$ are both positive and $L = \lim_{{n}\to{\infty} } \frac{a_n}{b_n} > 0$ then $\sum_{}^{} a_n$ will converge if $\sum_{}^{} b_n$ and $\sum_{}^{} a_n$ will diverge if $\sum_{}^{} b_n$ diverges. Does this rule also apply if $L$ diverges to...
  15. T

    MHB Determining the convergence or divergence of a sequence using comparison test

    I have this series: $$\sum_{k = 1}^{\infty} {4}^{\frac{1}{k}}$$ To solve this, I am trying to compare it to this series $$\sum_{k = 1}^{\infty} {4}^{k}$$ So, I can let $a_k = {4}^{\frac{1}{k}} $ and $b_k = {4}^{k}$ These seem to be both positive series and $ 0 \le a_k \le b_k$ Therefore...
  16. T

    MHB Determining the convergence or divergence of a sequence using direct comparison

    I have $$\sum_{n = 2}^{\infty} \frac{{(\ln\left({n}\right)})^{12}}{n^{\frac{9}{8}}}$$ We can compare it to $ \frac{1}{{n}^{\frac{1}{8}}}$. $ \sum_{n = 1}^{\infty} \frac{1}{{n}^{\frac{1}{8}}}$ diverges because $p < 1$ in this case. So, if I can prove that $...
  17. T

    MHB Determining whether an integral converges based on comparison

    I have this integral $$\int_{1}^{\infty} \frac{1}{(x + x^2)^\frac{1}{3}} \,dx$$ I think this is smaller than $$\int_{1}^{\infty} \frac{1}{(x^2)^\frac{1}{3}} \,dx$$ The latter converges since $p = \frac{2}{3}$ which is greater than 1. Therefore, since the first integral is smaller than the...
  18. anemone

    MHB Comparison between two numbers

    Compare the numbers $2^{2016}$ and $3^{201}7^{604}$.
  19. H

    Automotive Power Comparison: 5 Parts Air v 800 PSI w/ Diesel

    What is better for power? 5 parts air at 400 psi compression 10 inch bore by 30 inch stroke compared to 800 psi compression with 1 part air with 10 inch bore with 10 inch stroke? Same air fuel ratio in both With diesel? Which will be more power and which will be more efficient? And why?
  20. anemone

    MHB Comparison between X and Y

    Compare the numbers $X=(\log_2(\sqrt{5}+1))^3$ and $Y=1+\log_2(\sqrt{5}+2)$ and determine which is larger.
  21. anemone

    MHB Comparison between two power of numbers

    Prove that $8^{91}\gt 7^{92}$.
  22. L

    How do you do a Bode plot comparison with LTSpice?

    I'm trying to use LTSpice in order to fine tune LC circuits, but a road block I've hit is that when I run the simulation and generate a bode plot, the previous plot is overwritten, so I can't visually compare the effects of the L C changes. Some graphing programs have a function that let's you...
  23. JulienB

    I How does the limit comparison test for integrability go?

    Hi everybody! I have another question about integrability, especially about the limit comparison test. The script my teacher wrote states: (roughly translated from German) Limit test: Let -∞ < a < b ≤ ∞ and the functions f: [a,b) → [0,∞) and f: [a,b) → (0,∞) be proper integrable for any c ∈...
  24. M

    I Ideal Gases: O2 & H2 - Kinetic Energy Comparison

    Hello, I want to make sure I understand the following considering ideal gases. Assuming I have two different types of gases, say, O2 and H2 (each at thermal equilibrium), is it correct to say that the kinetic energy of the O2 gas equals to the kinetic energy of the H2 gas since they're both...
  25. anemone

    MHB Comparison between two numbers

    Determine, without the help of calculator, which of the following is bigger: 1016^{11}\cdot 3016^{31} versus 2016^{42}
  26. Ananay Wadehra

    Conditions of Big Bang & Light Speed Travel: Exploring Relativity

    According to Einsteins Theory of relativity if an object traveled at the speed of light, it's mass would become infinite, time would seem to stop relative to others and it length would become absolute zero. The same conditions were thought of at the Big Bang, when time didn't seem to have...
  27. K

    MHB C String Comparison: Debugging Error - "Hello" Output

    I am trying to compare a computer generated word to display the following however, when Quit is entered it produces the output "Hello". What is my error in the code? #include <stdio.h> #include <string.h> int main(void) { char userString[50]; strcpy(userString, "Quit"); /* Your...
  28. M

    Metal Tubing Strength and Weight Comparison Chart?

    I'll preface this with saying I'm an Industrial Designer, not an engineer. I also build workshop furniture as a hobby, which this question is in reference to. I'm building a motorcycle lift table. I'm curious, is there a chart that compares things like tubing material, size, strength and...
  29. L

    Understanding the Role of Calibration in Vapour Pressure Determination

    I am doing a lab which involves the determination of vapour pressure of a particular compound by Knudsen Effusion. Like other analytical methods it involves calibration but we are using the know vapour pressure of naphthalene because its in the accepted range. So we have an equation for the...
  30. Sergey_KGB

    A Po-210. Comparison of Gamma and Alpha spectrometry

    Hi Everybody! Just have read in the Report into the death of Alexander Litvinenko https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/493860/The-Litvinenko-Inquiry-H-C-695-web.pdf I'm very surpised to see that namely Gamma Spectrometry was used while only 1 in 100,000...
  31. Z

    MHB Series Convergence with Comparison Test

    Hey, I am working on Calculus III and Analysis, I really need help with this one problem. I am not even sure where to begin with this problem. I have attached my assignment to this thread and the problem I need help with is A. Thank you!
  32. ognik

    MHB Why is $U_n$ greater than $\frac{A}{n}$ for large enough values of $n$?

    Hi, my book says that $\lim_{{n}\to{\infty}} {n}^{p}U_n \rightarrow A \lt \infty, p \gt 1 $ means that $U_n \lt \frac{A}{{n}^{p}} $, which I can see But apparently $ \lim_{{n}\to{\infty}}n U_n = A \gt 0 $ means that $ U_n \gt \frac{A}{n} $ I know this is going to sound like a stupid...
  33. I

    GR Multibody Problem: Comparing Experimental Measurements

    I have a generic question on solution procedure. Suppose I consider a system of several point-like bodies interacting only via gravitation. I formulate PDE+ODE system, containing EFE and geodesic motion of the bodies. Since EFE do not define metric uniquely, I need to impose a particular...
  34. anemone

    MHB Comparison of value between two fractions

    Prove $\dfrac{3^{371}+5}{5^{247}+3}>\dfrac{2^{371}+3}{3^{247}+2}$.
  35. ognik

    MHB Series by comparison test

    Use the comparison test to see if \sum_{1}^{\infty}{\left[n\left(n+1\right)\right]}^{-\frac{1}{2}} converges? I tried n+1 \gt n, \therefore n(n+1) \gt n^2 , \therefore {\left[n(n+1)\right]}^{\frac{1}{2}} \gt n, \therefore {\left[n(n+1)\right]}^{-\frac{1}{2}} \lt \frac{1}{n} - no conclusion...
  36. anemone

    MHB Comparison between x²+y²+z² and 1/x²+1/y²+1/z²

    Let $x,\,y,\,z$ be positive real numbers such that $x+y+z=3$. Prove that $\dfrac{1}{x^2}+\dfrac{1}{y^2}+\dfrac{1}{z^2}\ge x^2+y^2+z^2$.
  37. Ellie Snyder

    Gravitational acceleration comparison

    Homework Statement Suppose an object of length “l” is located a distance “r” from a gravitating object of mass “M.” From physics you will learn that the gravitational acceleration is GM/r^2. Derive the difference in gravitational acceleration between distance “r” and distance “r+l” from the...
  38. S

    Comparison Test for improper integral

    Homework Statement use the comparison theorem to determine whether ∫ 0→1 (e^-x/√x) dx converges. Homework Equations I used ∫ 0 → 1 (1/√x) dx to compare with the integral above The Attempt at a Solution i found that ∫ 0 → 1 (1/√x) dx = 2 ( by substituting 0 for t and take the limit of the...
  39. F

    Comparison of 20" and 26" bicycles uphill

    Let's say you've got two electric bicycles both powered by identical 250W motors. Both are fixed gear. Both weigh about the same and have riders of the same weight. Both riders contribute no force to pedalling - all the work is done by the motors. The only difference is the first bike has 20"...
  40. sams

    Comparison Between Two Results

    Hello Everyone, I am performing comparisons between our obtained values with the values presented in the literature. These comparisons will be presented in our future paper. Usually, every relative error or a discrepancy below 10% is considered to be a "good" agreement in the Molecular Physics...
  41. D

    System of ODE - comparison with paper

    I have the following system of differential equations, for the functions ##A(r)## and ##B(r)##: ##A'-\frac{m}{r}A=(\epsilon+1)B## and ##-B' -\frac{m+1}{r}B=(\epsilon-1)A## ##m## and ##\epsilon## are constants, with ##\epsilon<1##. The functions ##A## and ##B## are the two components of a...
  42. P

    Comparison tests for series

    Comparison Test Consider the two infinite series ##\sum a_n## and ##\sum b_n## with ##a_n,b_n \geq 0## and ##a_n \leq b_n## for all ##n##. If ##\sum b_n## is convergent so is ##\sum a_n##. If ##\sum a_n## is divergent so is ##\sum b_n##. Limit Comparison Test Consider the two infinite series...
  43. A

    Comparison between quantum entanglement and a classical version

    What I understood from Quantum Entanglement (QE), is that measuring the spin of one of two entangled particles in one location gives the spin of the other particle in other location no matter how far is the later. What I can also understand is that the same concept is applicable in the classical...
  44. Sai-

    Bounding Argument for Comparison Test

    I have the sum, $$\sum_{n=1}^{\infty} \frac{1}{n^{3}}\sin(n \pi x) \text{, where }0 \leq x \leq 1$$ I have to show that the series converges, so I'm going to use the Comparison Test. $$ \text{If }0 \leq a_n \leq b_n \text{ then}$$$$\text{If }\sum b_n \text{ converges then }\sum a_n \text{ must...
  45. Kairos

    Distance Comparison: Converting 48 Distance Modulus to Meters

    hello I have problems with the distance units used in cosmology: I wonder where is located a distant supernova at 48 "distance modulus", compared to the Hubble radius. Far much less? please use meters (x10^25 m) thank you in advance rachid
  46. E

    Schools Which is Better for Theoretical Physics, Utrecht or Glasgow University?

    Hi everyone i am new to the forum. I am looking forward to a MSc in theoretical physics and have been offered place at Utrecht and Glasgow university. Unfortunately neither of the universities have a very detailed course outline at their sites (or its just my fault). I am interested in high...
  47. titasB

    Infinite Series Convergence using Comparison Test

    Homework Statement Determine whether the series is converging or diverging Homework Equations ∞ ∑ 1 / (3n +cos2(n)) n=1The Attempt at a Solution I used The Comparison Test, I'm just not sure I'm right. Here's what I've got: The dominant term in the denominator is is 3n and cos2(n)...
  48. M

    Randomized Complete Block Design - Scheffe Multiple Comparison

    Homework Statement I'm working on a problem in Design and Analysis of Experiments by Dean and Voss. It's Chapter 10 question 11 part c. We have an experiment with 2 treatment factors (each with three levels) and 1 blocking factor (with four levels. It's a randomized complete block design so...
  49. K

    2D-Diamond and 2D-Center Rectangular Lattice Comparison

    Hi All, Using (Mirror + Translation in 2D). I see that Diamond and Center Rectangular Lattice in 2D has the same Symmetry i.e: 1)Horizontal Mirror Plane 2)Vertical Mirror Plane 3)2-Fold Rotation Axis. and Diamond has Smaller Area. Then why we say Center Rectangular has higher Symmetry and we...
  50. R

    Vehicle COG comparison for longitudinal rollover

    Hi I am trying to compare which of the (2) models has the greatest stability longitudinaly. I have the COG height and longitudinal (axle split) Model A has it COG closer to the centre of the axles (longitudinal - further from rear axle 1,487l) but sits much higher (2,537 above axle centre) Model...
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