# I Lemma 1.2.3 - Ethan.D.Bloch - The Real Numbers and Real Analysis

#### anhtudo

Summary
What I don't understand is how he proves that G = N.
I don't think it is logical to let b = n as it can not be derived from the definition of G that b is in G.
Thanks. Related Topology and Analysis News on Phys.org

#### fresh_42

Mentor
2018 Award
It is written a bit confusing, but correct. Forget $b$.

We have $n\in G$ and $p=s(n)$. This implies $p \in G$ because there is some $n \in \mathbb{N}$ such that $s(n)=p$. Hence $s(n) \in G$. Therefore we have $1\in G$ and all successors of elements of $G$ are in $G$, too, i.e. $\mathbb{N} \subseteq G$.

• anhtudo

Thank you.

### Want to reply to this thread?

"Lemma 1.2.3 - Ethan.D.Bloch - The Real Numbers and Real Analysis"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving