# validity of convergent sequences with strict inequalities

• Mar 16th 2010, 06:06 PM
dgmath
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.
• Mar 16th 2010, 06:09 PM
Drexel28
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. $\displaystyle 0<\frac{1}{n}$
• Mar 16th 2010, 06:33 PM
dgmath
Quote:

Originally Posted by Drexel28
Of course not. $\displaystyle 0<\frac{1}{n}$

um, not sure I understand
• Mar 16th 2010, 06:34 PM
Drexel28
Quote:

Originally Posted by dgmath
um, not sure I understand

Define $\displaystyle x_n=0$ and $\displaystyle y_n=\frac{1}{n}$ then $\displaystyle x_n<y_n$ but $\displaystyle \lim\text{ }x_n=\lim\text{ }y_n=0$