find accumulation points of the following set in R^2
a) {(p,q) | p, q rational}
b) {m/n, 1/n)| m, n integers, n is not 0}
c) {1/n +1/m , 0 | m, n integers, n, m are not 0}
Please, help

Question

find accumulation points of the following set in R^2
a) {(p,q) | p, q rational}
b) {m/n, 1/n)| m, n integers, n is not 0}
c) {1/n +1/m , 0 | m, n integers, n, m are not 0}
Please, help

loser66 · Answer

@dumbcow

dumbcow · Answer

remind me what are accumulation points?

loser66 · Answer

it is not an isolated point

loser66 · Answer

and definition of isolated point is:
let x is the point, x is called isolated point iff the ball center x , radius r has no other point.

loser66 · Answer

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loser66 · Answer

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dumbcow · Answer

hmm i think you have overestimated my knowledge in higher mathematics :)

sorry i never took number theory and i haven't studied higher math in years

loser66 · Answer

I have solution here but I don't understand, can you interpret it?

loser66 · Answer

attachment

dumbcow · Answer

i can try, maybe we can reverse engineer it.... but i assume is has to do with set theory

loser66 · Answer

this is advanced calculus, not number theory.

loser66 · Answer

What I don't understand is $\sqrt2$ part, why they take it but not other rational number? Because it is the smallest one?

dumbcow · Answer

it seems arbitrary but by dividing by sqrt(2) it ensures that difference is less than "epsilon" and like you said sqrt (2) is smallest radical, so that the criteria is not too strict.

loser66 · Answer

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dumbcow · Answer

yeah

loser66 · Answer

Thank you very much. I think I got it. :)

loser66 · Answer

@eliassaab  can you help me understand part d?

loser66 · Answer

to me, if A ={(1/n+1/m, 0) | n $\neq 0$ and m$\neq 0$ }
I don't understand how the accumulation points are defined like that

loser66 · Answer

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