- #1
Danijel
- 43
- 1
So , what I was wondering about was a slight difference in notation, for which I am not certain if correct (mine, in particular.).
The induction axiom says: If M is a subset of ℕ, and if holds that:
a)1∈M
b)(∨n∈ℕ)(n∈M→s(n)∈M)
then M=ℕ.
Now my question is: why do we write (∨n∈ℕ)(n∈M→s(n)∈M), instead of (∨n∈M) s(n)∈M? Are these equivalent? Because, if we say n ∈ M, we consider that n∈ℕ and n∈M, since M⊆ℕ.
Thank you.
The induction axiom says: If M is a subset of ℕ, and if holds that:
a)1∈M
b)(∨n∈ℕ)(n∈M→s(n)∈M)
then M=ℕ.
Now my question is: why do we write (∨n∈ℕ)(n∈M→s(n)∈M), instead of (∨n∈M) s(n)∈M? Are these equivalent? Because, if we say n ∈ M, we consider that n∈ℕ and n∈M, since M⊆ℕ.
Thank you.
Last edited: