Thread: sequence convergence

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

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 , and if x is rational take

Tonio

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

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