- #1
Abraham
- 69
- 0
This isn't really hw. I need someone to explain a certain line in a proof:
" b2 [itex]\leq[/itex] [itex]\frac{1}{n}[/itex] for all n in the natural numbers. This implies that b2 [itex]\leq[/itex] 0 (a consequence of the Archimedean property). "
I don't see how the Archimedean is applied in this context. This is my understanding of the property: For real numbers x,y, x>0, there exists a natural number n such that nx > y.
I don't see how this proves b2 [itex]\leq[/itex] [itex]\frac{1}{n}[/itex] [itex]\Rightarrow[/itex] b2 [itex]\leq[/itex] 0.
Thanks
" b2 [itex]\leq[/itex] [itex]\frac{1}{n}[/itex] for all n in the natural numbers. This implies that b2 [itex]\leq[/itex] 0 (a consequence of the Archimedean property). "
I don't see how the Archimedean is applied in this context. This is my understanding of the property: For real numbers x,y, x>0, there exists a natural number n such that nx > y.
I don't see how this proves b2 [itex]\leq[/itex] [itex]\frac{1}{n}[/itex] [itex]\Rightarrow[/itex] b2 [itex]\leq[/itex] 0.
Thanks