9hmm i jus observed a function that satisfies this !
Is it possible to construct a continuous and differentiable curve in the cartesian plane such that both the co- ordinates can never be simultaneously rational ?
take 0 < x,y <1
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9 Answers
62I think no..
And i think this can be done by the fact that the no of rationals is countably infinite while irrationals is uncountably infinite
9ans
xn+yn =1
where n≥3 ,ε N
it follows from fermats last thm
1Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two.
but there can be rational numbers satisfying it
so this function can be simultaneously both co-od rational
1let a,b,c be three rational numbers satisfying a^n+b^n=c^n n>3
so X=a/c so x is rational
similarly y is rational
so we have two rational numbers possible
11@ rickdie, this is what Celestine wants...
x=ab
y=cd
(ad)n+(bc)n=(bd)n....Get it now?