# sequence convergence

• Oct 25th 2009, 06:19 PM
spikedpunch
sequence convergence
show that if x is a real number then there is a sequence of irrational numbers converging to x
• Oct 25th 2009, 07:56 PM
tonio
Quote:

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
• Oct 26th 2009, 07:04 AM
spikedpunch
I'm really shaky with my understanding of this stuff, so could you elaborate on what I would do with those sequences?
• Oct 26th 2009, 07:45 AM
tonio
Quote:

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