What is Word problem: Definition and 499 Discussions

In mathematics and computer science, a word problem for a set S with respect to a system of finite encodings of its elements is the algorithmic problem of deciding whether two given representatives represent the same element of the set. The problem is commonly encountered in abstract algebra, where given a presentation of an algebraic structure by generators and relators, the problem is to determine if two expressions represent the same element; a prototypical example is the word problem for groups. Less formally, the word problem in an algebra is: given a set of identities E, and two expressions x and y, is it possible to transform x into y using the identities in E as rewriting rules in both directions? While answering this question may not seem hard, the remarkable (and deep) result that emerges, in many important cases, is that the problem is undecidable.
Many, if not most all, undecidable problems in mathematics can be posed as word problems; see the list of undecidable problems for many examples.

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  1. P

    Connecting Points with a Curved Equation: Solving a Calculus Word Problem

    1.A line segment extends horizontally to the left from the point (-1, -1). Another line segment extends horizontally to the right from the point (1, 1). Find a curve of the form y = ax^5 + bx^3 + x that connects the points (-1, -1) and (1, 1) so that the slope and curvature of the curve are...
  2. B

    MHB Solving D.E Word Problem: Radium Decompose, Half Life 1600, 200 Years

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  3. A

    MHB Finding Constraints in Polynomial Data: How Many Linear Equations Are Needed?

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  4. L

    MHB Derivative word problem - have I got the wrong solution?

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  5. B

    MHB Find Difference in Total Cost for Engagement Ring at 2 Jewelers

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  6. B

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  7. paulmdrdo1

    MHB Another word problem involving a linear system.

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  8. B

    MHB Algebra word problem: the angle between the hands of a clock

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  9. paulmdrdo1

    MHB Clock Word Problem: Solve in 2 Steps w/ Hints

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  10. K

    MHB Solve Ratio Word Problem: Find Value of x

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  11. O

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  12. C

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  13. B

    MHB Can You Solve This Set Theory and Binary Number Problem?

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  14. T

    What to do when you can't remember a formula for a word problem?

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  15. U

    Calculating Foraging Energy Balance: Solving for Net Change in Energy Level

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  16. J

    Solve Annuity Word Problem: Debt of $82423.55

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  17. O

    DE word problem: fluid in a tank

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  18. B

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  19. J

    MHB Math Word Problem - price and yield of T-bill

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  20. L

    Operations research word problem help appreciated

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  21. A

    Word problem : Finding the time in which workers can do a job .

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  22. T

    Word Problem Confusion: Am I Right or Nitpicky?

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  23. J

    Trigonometry Word problem with angles of elevation

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  24. N

    MHB How Do You Calculate Profit from Selling Oranges by the Box?

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  25. E

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  26. Petrus

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  27. H

    Solve Vector Word Problem with Tow Truck: Work Done in Joules

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  28. I

    Physics Diff'eq Word Problem, Help Setting Up

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  29. D

    Buying and Selling Beef Word Problem

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  30. D

    Quadratic Functions Word Problem

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  31. Feodalherren

    What is the speed of the lighthouse beam along the shoreline?

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  32. Petrus

    MHB Word problem involving counting

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  33. P

    I have a question about an airspeed/groundspeed word problem

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  34. T

    Solving Word Problem Logs with Population of Deer Increase from 800 to 1800

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  35. W

    Colomb's Law Word Problem

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  36. twoski

    Optimizing Expected Cost for Traveling to an Appointment

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  37. M

    Exponential growth word problem, pie.

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  38. S

    Differential Calculus Word Problem

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  39. L

    MHB Help with exponential function word problem

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  40. C

    Maxima and Minima of two-variable functions word problem

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  41. L

    Differential equation: word problem

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  42. J

    Projectile Motion word problem from Calc III course (finding height of a wall).

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  43. N

    Distance and speed word problem. Introduction to vectors.

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  44. P

    Difficult vector word problem final step

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  45. P

    Vector addition word problem question

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  46. P

    Kinematics of Constant acceleration word problem

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  47. L

    Word problem: Finding area of a growing triangle.

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  48. T

    Differentiation word problem (basic)

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  49. S

    Exponential distribution word problem

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  50. L

    MHB Simultaneous equation word problem

    "A school mathematics department has 1440 euros to buy textbooks. Maths for All volume 1 costs 70 euros. Maths for All volume 2 costs 40 euros. The department wants twice as many copies of volume 1 as volume 2. How many of each volume can they buy?" I got up to that the first equation is 70x +...
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