- #1

kingstrick

- 108

- 0

## Homework Statement

Show that the limit point of Sn:={1-1/n} is 1.

## Homework Equations

We are prohibited from using epsilon and delta

## The Attempt at a Solution

Let Sn:= {1-1/n} and U be any open interval from (a,b) where a<1<b. Observe that Sn is always [itex]\leq[/itex] 1. Since a<1 is linearly ordered, there is a positive number d between a and 1 such that a<d<1 and 1/d > 1. Then since d < 1,

d-1 < 1-1

d-1 < 0

(d-1)/d < 0 --> (d-1)/d = 1 - [itex]\frac{1}{d}[/itex] and ...

i am stuck, it appears that i shown my Sn is always less then zero making my limit point zero not one. Any help would be appreciated.