# Math Help - sequence convergence

1. ## sequence convergence

show that if x is a real number then there is a sequence of irrational numbers converging to x

2. Originally Posted by spikedpunch
show that if x is a real number then there is a sequence of irrational numbers converging to x
If x is irrational take $\,\,a_n=x\frac{n+1}{n}$ , and if x is rational take $\,\, x\frac{\pi n+1}{\pi n}$

Tonio

3. I'm really shaky with my understanding of this stuff, so could you elaborate on what I would do with those sequences?

4. Originally Posted by spikedpunch
I'm really shaky with my understanding of this stuff, so could you elaborate on what I would do with those sequences?
What "to do" with them? Well, just convince yourself that indeed both of them are irrational sequences and that both converge to x...what else?

Tonio