Guys what are the accumulation points of the rationals?

>>8953516
what is your definition of accumulation point?

>>8953526
let E be a subset of X, and a a point belonging to X
a is an accumulation point of E if every ball centered around a and of radius r > 0 contains a second point b != a such that b belongs to E

sorry if its awkward I'm translating from french

>>8953531
and X is a metric space

>>8953531
this is usually called a limit point
anyway, every real number x is a limit point of Q, because every interval (hence any neighborhood of x) contains a rational number

>>8953541
nice that was my intuition as well.
by the same logic every interval of R contains an infinite number of real numbers, so every real number is a limit point of R. correct?

>>8953548
right. this is summed up by saying that R is a perfect set (don't know if you've heard this term)

>>8953516
Ever since gone girl I still really want to punch that bitch in the face

>>8953516
>>8949243