Question

1 + 1 = ? no really, wat interpretation of S(1) (as in successor function)

Answer 1

this is a hard one!! XD

Answer 2

S1=S

Answer 3

good

Answer 4

1 apple + 1apple=2apples

Answer 5

I don't think he means 1+1 in a literal way....right?

Answer 6

qwarty+alax=SH

Answer 7

i'm just wondering if he means 1+1 in a much different matter than 1+1=2

Answer 8

do we define S(1)=2? and is S(9)=10 due to decimal representation?

Answer 9

WOIW
S(1)=10
S(2)=100 you mean that?>

Answer 10

I am sure this isn't a spam post now? :P

Answer 11

S(x) whewre x is the number of digits after decimal?

Answer 12

no, not really @AlexandervonHumboldt2 ... I am wondering what exactly a successor function is

Answer 13

successor function is this-
\(S(n)=n+1\)
n\(\in\) natural number
its defined for natural numbers

Answer 14

yes, but dosen't the successor function define addition?

Answer 15

if it does, doesn't that mean we have to avoid using addition to define the successor function?

Answer 16

what do you mean by defining addition here?

Answer 17

https://en.wikipedia.org/wiki/Peano_axioms#Addition

Answer 18

okay it does

Answer 19

Any ideas @imqwerty ? started out with a joke but I'm actually kinda curious as to how the successor function is defined...

Answer 20

can we just say that S(x) is the next number to x
or S(x) denotes number quantities lying in the set [0,x]
?

Answer 21

what is the next number to x? you see my problem now?
I don't know very much about number theory...
Is the well-ordered nature of the natural numbers an axiom? if it is, does the successor function just denote the next element in a set?

Answer 22

And more about well-ordering in general: is there only exactly one way to order the natural numbers? why is S(x) unique for a given x in N?

Answer 23

which business is axiomatic and which follows from the axioms?

Answer 24

number are arranged in ascending or descending order and thus there is only one way to arrange them and the arrangement must be taken as an axiom or assumption because in the ascending or descending order theory the question that why 3 is greater than 2 or smaller than 5 will arise and we can't really give a legit reason
because successor function S(n) is nothing but n+1 which is simply the next number lying to n it must be unique because while arranging the numbers only 1 number can take place to the next[ascending side] of n

Answer 25

okay... and the existence of a successor function is in and of itself an axiom?