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Homework Help: What does the symbol ≡ mean?

  1. May 4, 2010 #1
    What does the symbol ≡ mean?

    For example:

    [tex]max_{x}[F(x,\alpha):g(x)\leq b,x\geq 0] \equiv G(\alpha,b)[/tex]

    Thanks for your help.

  2. jcsd
  3. May 4, 2010 #2

    D H

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    Staff Emeritus
    Science Advisor

    In this case, it appears to means "defined as". It can also mean "identically equal to", as for example [itex]\sin^2 \theta + \cos^2\theta \equiv 1[/itex].
  4. May 4, 2010 #3
    So in your trigonometric example, its like saying "it may as well be 1, but its not exactly 1". Is this what it means?
  5. May 4, 2010 #4

    D H

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    Staff Emeritus
    Science Advisor

    No! In the trigonemtric example in means, in English, that the sum of the squares of the sine and cosine of an angle is always exactly one. It is an identity.
  6. May 4, 2010 #5


    Staff: Mentor

    No, not at all. It means "identically equal to" in this identity. This means that the left side of this identity is equal to 1 for all values of theta.

    Here are a couple of examples to distinguish = from [itex]\equiv[/itex].

    2x + 4 [itex]\equiv[/itex] 2(x + 2). This equation is an identity, one that is true for all values of x. You cannot solve for x in this equation.

    2x + 4 = 8. This equation is a conditional equality, one that is true only for one value of x. You can solve for the value of x in this equation.
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