Why the natural numbers begin with 1
Why the natural numbers begin with 1
We first learn to count beginning with 1.
Addition in can be defined purely in terms of the successor function
The additive identity is not a direct result of the successor function.
Zero is not a primitive concept
Some proofs are marginally simpler because no consideration of the spacial case of is required.
0
The integers are expressible using only ordered pairs of natural numbers.
The commutative, associative and cancellative laws of addition can be derived in .
The principle of induction can be established in
The principle of recursion can be established in
The commutative, associative and cancellative laws of multiplication can be established in without exception.
The well-ordering of can be established.
Zero arises naturally when extending to
.
The domains of positivity ,, can all be constructed without introducing .
0
Segments such that begin with the non-successor .
n
Size[]=n
n
1
Pointing at the first number of the most primitive set of numbers and uttering the word zero is silly.