Recent content by philbein

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    Equivalence Relation and a Function

    Homework Statement Suppose that A is a nonempty set and R is an equivalence relation on A. PROVE that there is a function f with A as its domain such that for x and y in A, xRy (x is related to y) if and only if f(x)=f(y) Homework Equations Equivalence relations are relations that...
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    Is there an integer divisible by 1989 with 1990 as its last four digits?

    Finally figured it out. Not an easy problem. Thanks for all the help. Couldn't have done it without the help. Thanks again.
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    Is there an integer divisible by 1989 with 1990 as its last four digits?

    Ok. I'm still confused.
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    Is there an integer divisible by 1989 with 1990 as its last four digits?

    I'm sorry. I'm still not seeing what this does. Either way, I am still left with a remainder of 1.
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    Is there an integer divisible by 1989 with 1990 as its last four digits?

    Should I add 1989 to the remainder or to the orignal number that I had divided by 1989?
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    Is there an integer divisible by 1989 with 1990 as its last four digits?

    Homework Statement Prove that there exists an integer divisible by 1989 Such that it's last four digits are 1990. Homework Equations Pigeonhole Principle where if we have k+1 items and k holes, two items go in one hole. The Attempt at a Solution Ok. I called my professor for...
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    Real Analysis Question involving the definition of the derivative

    Homework Statement Suppose f:(a,b) to R(Real numbers), is differentiable at any point x that is in the interval (a,b). Prove that lim(as h goes to 0) of (f(x+h)- f(x-h))/(2h) exists and equals the derivative of f(x) ( which is f '(x)). Give an example of a function where the limit exists...
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    Need help on some problems w/ accumulation points

    Homework Statement Give an example of a set with exactly two accumulation points. Homework Equations We can use the definition of accumulation points The Attempt at a Solution I really have no idea where to get started on this. If I could get a hint that would be great thank you
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    But if x=0 then x=-0So we conclude that 0=-0Is -0 a Real Number?

    I need help urgently asap proving that -0=0 Homework Statement Prove that 0=-0 Homework Equations We Can use only the following axioms for Real Numbers (x+y)+z=x+(y+z); (xy)z=x(yz) x+y=y+x; xy=yx x(y+z)=(xy)+(xz) The Additive Identity 0+x=x The Additive Inverse for all x in the...