What is Rational: Definition and 626 Discussions

Rationality is the quality or state of being rational – that is, being based on or agreeable to reason. Rationality implies the conformity of one's beliefs with one's reasons to believe, and of one's actions with one's reasons for action. "Rationality" has different specialized meanings in philosophy, economics, sociology, psychology, evolutionary biology, game theory and political science.

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  1. D

    When find LCD for a rational expressions.

    Ok I have to find the Lowest Common Denominator for 3 ration expressions. I don't think the numerators are important so Ill just leave them out. The denominators are x^2 - 4 and x -2 I got the LCD as x-2. correct? When finding the LCD in expressions like this you just have to factor...
  2. J

    Maximum of rational functions

    Suppose 2 cuadratic functions: ax^2+bx+c, dx^2+ex+f. Suppose that the first one is upside with its minimum above the x line reference, and the second one is downside with its maximum above the x reference, and suppose that the two functions intersect at two points that pass through straight line...
  3. L

    Rational and Irrational Numbers

    I need to show that a rational + irrational number is irrational. I am trying to do a proof by contradiction. So far I have: Suppose a rational, b irrational. Then a = p/q for p, q in Z. Then a + b = p/q + b = (p + qb) / q But I don't know where to go from here because I still have a...
  4. B

    Integrating Rational Functions: How to Solve Challenging Integrals?

    How do I solve this integral?? (it's in the attachment) (my-efforts.gif just explains a failed attempt)
  5. S

    Can pi or e ever be rational in a different number system?

    Hello, I doubt it, but is there any number system (base) where π or e run out of digits?
  6. A

    Rational Expressions loooong BUT NEED HELP

    state the vertical asymptote(s), x-intercept(s), y-intercept(s), domain and range of f(x)=(1)/(4x^2)-1 ok I factored the denominator and got (2x+1) (2x-1) I solved for x, so the x-intercepts are x=-1/2, and x=1/2 for only (4x^2)-1 the reciprocal function has no x-intercepts. Sub in x=0 to...
  7. F

    How Do You Solve Complex Rational Equations Without Proper Guidance?

    Ok, so before every says that I am just looking for answers, I would like to say my teacher has been on "stress leave" for the past 5 weeks and we have been tought by a very bad "math" teacher Im having a hard time with Rational Equations, I guess because I have no notes on it :cry: So I am...
  8. E

    Questions concerning, logs, rational funtions, and trig.

    Allright, I have a math test next week and there's some things i want to clear up before i take it. I can't use a calculator btw. 1) We've learned a lot about testing symmetry (y-axis, x-axis, origin). It seems on most problems we just test y and origin symm. When do you know you shoudl test...
  9. T

    What number is rational and irrational

    When is x rational and irrational? Also When is r positive and negative? :confused:
  10. agro

    Irrationality of Rational Exponents

    What's actually the definition of a^{m/n} where m and n are integers and a is any real number? Suppose I define it as the n-th square root of a^m. Wouldn't it be inconsistent with other stuffs? What stuffs? For example, a^1 is supposed to be a. But 1 = 2/2 and, using my earlier definition...
  11. S

    Solving Rational Number Equation | Express x as Ratio of Integers

    Suppose a, b, and c are integers and x, y, and z are nonzero real numbers that satisfy the following equations: xy/x+y = a xz/x+z = b yz/y+z = c Is x rational? If so, express it as a ratio of two integers. I am pretty sure x is rational, but I don't know how to get the ratio. I am...
  12. F

    Rational expression of two linear expression

    Hello! Are all rational expression of two linear expression, say f (x) = (x + 3)/(x - 3), bijective? How will x = 3 affect the condition of a bijective function?
  13. S

    Fractions and Rational Numbers

    I got a few questions. First of all, I reduced 3715/990 to 743/198. Is that reduced all the way? Second, using the natural number, 1-10, as either the numerator or denominator of a fraction, there is 100 fractions, 1/1, 2/1,...,10/1, 1/2, 2/2,...10/10. How many of these reduce to integers. I...
  14. D

    An accurate representation of Irrational and rational numbers

    Is there an accurate way to write the value of an Irrational number? If there is no an accurate way to write the value of an Irrational number, then can we conclude that no irrational number has an exact place on the real line? And if there is an exact place to an irrational number on the...
  15. E

    Proof: Numbers with repeating blocks of digits are rational

    Hi everyone, I need to prove that any number with a repeating block of digits is a rational number. Someone told me I should first find a method of constructing a rational number in the form a/b from a number with repeating blocks of digits (and to do it with very 'easy' numbers first). I'm...
  16. I

    The Rational Choice: Is Humanity Always Involved?

    "The rational choice is not always the one with the most humanity in it" Give me your point of view about this quotation. You may agree or disagree with it.
  17. JasonRox

    How Do You Differentiate Between Polynomial and Rational Algebraic Functions?

    How can you tell the two apart? Here are some examples in the book: 1. 3x^3 + 2x + 1 2. 3x^2 + (x + 1)^1/2 3. \frac{2x + 3}{x^2 + 1} 4. (\frac{x}{x + 1})^X
  18. E

    Some theorem regarding rational numbers

    If y>x where x and y are both elements of the reals, but x is also irrational, I must prove that there is a rational number z such that x<z<y. I can only show this is true when x is rational. How do you add something to an irrational number to make it rational?
  19. Dissident Dan

    The Rational Animal: Exploring the Limits of Human Rationality

    Most of you have probably heard a phrase along the lines of "man the rational animal". I think that it is fairly obvious that this phrase is meant to refer to the the idea that man has rational abilities, not that he is impervious to irrational emotions. Perhaps it is supposed to suggest that...
  20. K

    Integration of rational functions

    How do I solve the integration of a rational function such as: x^2 - 6x - 2 (x^2 + 2)^2 If possible, please list the general rule of solving, I DO NOT want the answer, I simply want to know the way of solving it. Thanks in advance! So far I got to the part where A = 1, B = -6 and...
  21. K

    Integration of rational functions

    How do I solve the integration of a rational function such as: x^2 - 6x - 2 (x^2 + 2)^2 If possible, please list the general rule of solving, I DO NOT want the answer, I simply want to know the way of solving it. Thanks in advance!
  22. I

    Integral of rational functions

    Can someone pls help me solve this integral? integral of (6x^2-13x-43)dx/(x^3-1x^2-8x+12) it's supposed to be solved using partial fractions, but I am having trouble factoring the denom correctly so I can apply it... Thanks
  23. D

    Can "Real Powers" Give You a Rational Number?

    can e to any real powers give you a rational number?
  24. Loren Booda

    Can the ratio of two irrationals be rational?

    Does there exist a rational number ratio for any two irrational numbers?
  25. S

    Integrating rational functions

    I've just finished reading the section on partial fraction integration from my text. The book describes how all rational functions can be integrated by performing a partial fraction decomposition and subsequently integrating the partial fractions using methods that are already known. I tried to...
  26. Loren Booda

    Fractals of rational dimension and fractals of integral powers

    What generalizations can be made concerning fractals of nonzero rational dimensions M/N (where M and N are nonzero integers)? How does a fractal of non-integral dimension F compare geometrically to a fractal of dimension GF, where G is a nonzero integer?
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