The standard axioms for defining addition and multiplication are:
a+0=a
a+Sb = S(a+b)
a*0 = 0
a*Sb = a+(a*b).
(Here, Sx means "the number that comes after x")
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Multiplication by an integer is the same as repeated addition.
Multiplication is repeated addition.
For addition, 0 and for multiplication, 1.
a multiplication form is repeated addition
The set of integers is closed with respect to multiplication and with respect to addition.