Every convergent sequence is Cauchy but converse is not true.

[@Azure4509]

Sir kia kisi bhi sequence ki convergence k liye ye baat zaroori hai k wo jis set se li hai oska limit os set mein mojod ho? Q k real analysis mein agar koi sequence rational set se li ho to agar oska limit irrational aye to phir wo sequence converge hogi? Kisi bhi Sequence k convergence k liye kia sirf yahi shart kaafi nahi k oska limit exist kary? Sir please reply

[@ukirdes.r.8770]

I regret for the late reply. Sequence ko hm convergent kehte hai jb uska limit exist ho but wo limit jis set se sequence li hi usme hona bhi zaroori h.
e.g {1/n:n is real number}
ye sequence real number me to convergent h lekin same sequence hm (0,1) le to is set me convergent nhi j q ki 1/n ka limit 0 h jo R me to mil rha hai lekin (0,1) me nhi milta.

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