validity of convergent sequences with strict inequalities

Suppose there are two sequences {xk} and {yk} of reals such that {xk} converges to x, and yk converges to y.

I know that if xk >= yk for all k>=m, then x>=y.

However, if xk>yk for all k>=m, would x>y hold true as well?

I'm rather bad with understanding subtle differences when it comes to strict inequalities, so please provide a reason as well.

Quote:

---

Originally Posted by dgmath

Suppose there are two sequences {xk} and {yk} of reals such that {xk} converges to x, and yk converges to y.

I know that if xk >= yk for all k>=m, then x>=y.

However, if xk>yk for all k>=m, would x>y hold true as well?

I'm rather bad with understanding subtle differences when it comes to strict inequalities, so please provide a reason as well.

---

Of course not.

Quote:

---

Originally Posted by Drexel28

Of course not.

---

um, not sure I understand

Quote:

---

Originally Posted by dgmath

um, not sure I understand

---

Define and then but