Thread: Is this correct?

1. Is this correct?

Statement: For every n>1 that is in N(Natural numbers) there exist k in N that k+1=n

So this is how I proved , if n>1 then n-1 is in N too because n-1>0, so there exist k in N that k=n-1 and from here we got n=k+1

is this correct? thank you

2. Re: Is this correct?

Assuming that the standard arithmetic operations have been defined on your set (so "n+ 1" does not just refer to the "successor of n" from Peano's axioms), yes, that is valid.

3. Re: Is this correct?

I am going over my lecture notes for my exam, and there are a lot of things that confuses me at this point, when I read analysis books, when they define Peano's axioms,for the successor of n they write P(n) because arithmetic operation isn't defined for N, but in my lecture notes we wrote n+1 and we haven't defined any arithmetic operation on N. But what we did was to define what field is and operation in addition and in multiplication, however N is not a field so I can't say that those operations that is defined for fields are valid for N too, so this is why I am confused... So did we define it or not? It looks like we didn't however we wrote n+1...

4. Re: Is this correct?

From A (not THE) def of natural numbers:

1=1
2=1+1
3=1+2
.
.
Every natural number =k+1 for some k.